Math, asked by tanya6677, 1 year ago

If (sin theta-cos theta)=0 then evaluate(sin^4theta+cos^4 theta)​


sivaprasath: = 4
sivaprasath: 2/4 ** = 1/2

Answers

Answered by Kevqn11
2

Answer: sin⁴Ф + cos⁴Ф = -1/2

Step-by-step explanation:

sinФ - cosФ = 0

by squaring both the sides, we get -

sin²Ф + cos²Ф - 2sinФcosФ = 0

⇒ sin²Ф + cos²Ф = 2sinФcosФ  -eq.1

but sin²Ф + cos²Ф = 1 using identity.

so, ⇒ sinФcosФ = 1/2

Now squaring both sides of eq.1, we get

⇒sin⁴Ф + cos⁴Ф +2sin²Фcos²Ф = 4sin⁴Фcos⁴Ф

⇒sin⁴Ф + cos⁴Ф + 2(1/2)² = 4(1/2)⁴

⇒sin⁴Ф + cos⁴Ф = 1/4 - 1/2

⇒sin⁴Ф + cos⁴Ф = -1/2

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