4
Question
If sinθ-cosθ=0 then the value of (sin⁴θ+cos⁴θ)?
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Solution
we have, sin θ - cos θ = 0
⇒ sin θ = cos θ
⇒ tan θ = 1
⇒ tan θ = tan 45
⇒ θ = 45
now.
sin^4θ + cos^4θ
= (1 / √2)^4 + (1 /√2)^4 = 1 / 4 + 1 / 4 = 1 / 2 [ as, sin 45= cos 45= 1 / √2 ]
answer = 1/2 = .5
we have, sin θ - cos θ = 0
⇒ sin θ = cos θ
⇒ tan θ = 1
⇒ tan θ = tan 45
⇒ θ = 45
now.
sin^4θ + cos^4θ
= (1 / √2)^4 + (1 /√2)^4 = 1 / 4 + 1 / 4 = 1 / 2 [ as, sin 45= cos 45= 1 / √2 ]
answer = 1/2 = .5
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