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( * ) If sin theta + cos theta = a and tan theta + cot theta = b then b (a square – 1) =

( * )
If sin theta + cos theta = a and tan theta + cot theta = b then b (a square –  1) =

Grade:11

2 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
9 years ago
Hi,

Folow the following steps :

Put the values of a & b in the expression and expand the second bracket , u will see that the remaining term in second bracket is 2SINxCOSx. Now multiply this term with the first bracket and take the terms out which are common . You will see that the final answer is reducing to 2 after you applied SIN^2+COS^2=1 identity.
pradipta kumar sahoo
13 Points
6 years ago
b=tan theta+cot theta
  =sin theta/cos theta+cos theta/sin theta
=sin^2 theta+cos^2 theta/sin theta*cos theta
=1/sin theta*cos theta
a=sin theta+cos theta
b*(a^2-1)=1/sin theta*cos theta(1+2sin theta*cos theta-1)
            =2

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