Question

If sin theta + cos theta = root2 sin (90-theta). find tan
theta

Answer 1

Hey there !

Solution:

Given: Sin A + Cos A = √2 Sin ( 90 - A )

To Find: Tan A = ?

Proof :

=> Sin ( 90 - A ) = Cos A

=> Sin A + Cos A = √2 Cos A

=> Sin A = √2 Cos A - Cos A

=> Sin A = Cos A ( √2 - 1 )

=> Sin A / Cos A = ( √2 - 1 )

=> Tan A = ( √2 - 1 )      [ ∵ Sin A / Cos A = Tan A ]

Hence ( √2 - 1 ) is the value of Tan A.

Hope my answer helped !

Answer 2

Hope it will help you.