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