Question

If sin theta _ cos theta =0 then find the value of sin4theta + cos4theta

Answer 1

Answer:

Step-by-step explanation:

sinθ -cosθ =0

To find :- sin⁴ θ -cos⁴θ

sin²θ + cos²θ = 1

( sinθ - cosθ )²+ 2sinθ.cosθ =1

0 + 2sinθ.cosθ =1

sinθ.cosθ =1/2

sin⁴θ + cos⁴ θ

= (sin²θ)² + (cos²θ)²

=( sin²θ + cos ² θ )² - 2sin²θ.cos²θ

= 1 - 2sin²θ.cos²θ

= 1 - 2 * (1/2)²

=1 - 2*1/4

=1 -1/2

=1/2 ........ans.