No products in the cart.

Prove that 1/2tan-1x=cos-1√1+√1+x2/2√1+x2

CBSE, JEE, NEET, CUET

Question Bank, Mock Tests, Exam Papers

NCERT Solutions, Sample Papers, Notes, Videos

Install Now

Prove that

1/2tan^-1x=cos^-1√1+√1+x²/2√1+x²

Posted by Dishaant Pandit 8 years, 2 months ago

CBSE > Class 12 > Mathematics

1 answers

Naveen Sharma 8 years, 2 months ago

Ans.

${1\over 2}tan^{-1}x = cos^{-1} (\sqrt {1 +\sqrt{1+x^2}\over 2\sqrt{1+x^2}})$

$taking \space LHS, put \space x = tan \theta$

=> $cos^{-1} (\sqrt {1 +\sqrt{1+tan^2\theta}\over 2\sqrt{1+tan^2\theta}})$

=> $cos^{-1} (\sqrt {1 +\sqrt{sec^2\theta}\over 2\sqrt{sec^2\theta}})$

=> $cos^{-1} (\sqrt {1 +{sec\theta}\over 2{sec\theta}})$

=> $cos^{-1} ({\sqrt {1 +cos\theta\over 2}})$

=> $cos^{-1} ({\sqrt { cos^2{\theta\over 2}}})$

=> $cos^{-1} ({ cos{\theta\over 2}})$

=> $LHS = {\theta\over 2}$

$Taking \space RHS, put \space x = tan\theta$

=> ${1\over 2} tan^{-1}({tan \theta })$

=> $RHS = {{\theta \over 2}}$

RHS = LHS

Hence Proved

2Thank You

ANSWER

Related Questions

Find the second order derivatives of the functions x²+3x+2

Posted by Sanjna Gupta 9 months, 3 weeks ago

CBSE > Class 12 > Mathematics

4 answers

This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

Few rules to keep homework help section safe, clean and informative.

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Tumngam Karbak 10 months, 1 week ago

CBSE > Class 12 > Mathematics

0 answers

Y=sin√ax^2+√bx+√c

Posted by Karan Kumar Mohanta 10 months ago

CBSE > Class 12 > Mathematics

0 answers

Three friends Ravi Raju

Posted by Sneha Pandey 10 months, 2 weeks ago

CBSE > Class 12 > Mathematics

0 answers

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Suchitra Jain 9 months, 3 weeks ago

CBSE > Class 12 > Mathematics

0 answers

What is the maximum value of the function sin x + cosx

Posted by Xxxxxx Xx 9 months, 3 weeks ago

CBSE > Class 12 > Mathematics

0 answers

Y= 1/2 [tan¯¹(2x/1-x²) + 2tan¯¹(1/x)

Posted by Charu Baid 9 months, 3 weeks ago

CBSE > Class 12 > Mathematics

0 answers

What is the maximum value of sinx + cos x

Posted by Xxxxxx Xx 9 months, 3 weeks ago

CBSE > Class 12 > Mathematics

3 answers

Find all vectors of magnitude 10√3 that are perpendicular to the plane of i+2j+k and -i+3j+4k

Posted by Sanjay Kumar 10 months, 1 week ago

CBSE > Class 12 > Mathematics

0 answers

Don't post personal information, mobile numbers and other details.
Don't use this platform for chatting, social networking and making friends. This platform is meant only for asking subject specific and study related questions.
Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
Ask specific question which are clear and concise.

Remember the goal of this website is to share knowledge and learn from each other. Ask questions and help others by answering questions.

Posted by Neemisha Gusain 10 months, 1 week ago

CBSE > Class 12 > Mathematics