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Prove that (sin theta + Cosec …

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Prove that (sin theta + Cosec theta)^2+(cos theta +sec theta)^2 = 7+ tan^2 theta + cot^2 theta

Posted by ?Roman ? 6 years, 3 months ago

CBSE > Class 10 > Mathematics

8 answers

Aadya Singh ? 6 years, 3 months ago

LHS = (sin^2 theta + cosec^2 theta + 2×sin theta × cosec theta) + ( cos^2 theta + sec^2 theta + 2×cos theta × sec theta)
=> (sin^2 theta + cos^2 theta)+ cosec^2 theta + sec^2 theta + 2×sin theta×cosec theta + 2 ×cos theta × sec theta
=> 1 + (1+cot^2 theta) + (1+tan^theta) + (2×sin theta× 1/sin theta ) + ( 2× cos theta × 1/cos theta)
=> 7 + cot^2 theta + tan^2 theta...
Now, LHS = RHS
So, it's prove....

Shreya ... 6 years, 3 months ago

Wlcm..?muh kyu bana rkha h

?Roman ? 6 years, 3 months ago

Thank you ?

?Roman ? 6 years, 3 months ago

??

Pk . 6 years, 3 months ago

Cosec ko sin.....and sec ko cos me change kar ke......do as given ...i mean perform their square....you definately get it,????

Shreya ... 6 years, 3 months ago

Used identity=> sin theta cosec theta=1, cos theta sec theta=1, sin^2theta+cos^2theta=1, cosec^2theta=1+cot^2theta.

Shreya ... 6 years, 3 months ago

LHS= (sin theta+cosec theta)^2+(cos thetha+ sec thetha)^2
(sin^2theta+coscec^2theta+2 sin theta cosec theta) + (cos^2theta+ sec^2theta+2cos theta sec theta)
(sin^2theta+cosec^2theta+2) + (cos^2theta+sec^2theta+2)
(sin^2theta+cos^2theta)+4+(cosec^2 thetha+sec^2theta)
1+4+(1+cot^2theta)+(1+tan^2 theta) = (7+tan^2theta+cot^2)

?Roman ? 6 years, 3 months ago

Anybody here solve this ??

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