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If 1+sin^2theta=3sintheta*costheta then prove that tantheta=1 …

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If 1+sin^2theta=3sintheta*costheta then prove that tantheta=1 or 1/2

Posted by Satyam Kumar 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years ago

1+sin^2 theta=3 sin theta cos theta (we know that sin^2 theta + cos^2 theta =1)

= ( sin^2 theta + cos^2 theta ) + sin ^2 theta = 3 sin theta cos theta

= sin^2 theta + cos^2 theta + sin ^2 theta = 3 sin theta cos theta

= cos^2 theta + 2 sin^2 theta = 3 sin theta cos theta

On dividing by cos^2 theta, we get

= 1 + 2 tan^2 theta = 3 tan theta

Let tan theta = b

2b^2 - 3b + 1 = 0

= (2b-1)(b-1) = 0

b = 1 or 1/2

So, tan theta = 1 or 1/2.

0Thank You

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CBSE > Class 10 > Mathematics