1.

if sin theta minus cos theta is equal to zero then the value of sin 4 theta + cos 4 theta is equal to what​

Answer»

Answer:

3√2

Step-by-step EXPLANATION:

sinθ -cosθ =0

squaring on both sides ,

(sinθ - cosθ)² = (0)²

sin²θ + cos²θ - 2 sinθcosθ  = 0

1 - 2 sinθcosθ = 0

2 sinθcosθ=1

sinθcosθ = 1/2    

(sin4θ + cos4θ )²  = 16sin²θ + 16cos²θ +2 sinθcosθ

(sin4θ + cos4θ )²   =16 (sin²θ +cos²θ) + 2×(1/2)

(sin4θ + cos4θ )²  = 16+2

(sin4θ + cos4θ )²  = 18

sin4θ + cos4θ = √18

sin4θ + cos4θ = √2 ×√9

sin4θ + cos4θ = 3√2

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