Advertisements
Advertisements
Question
If sin θ – cos θ = 0, then find the value of sin4 θ + cos4 θ.
Advertisements
Solution
sin θ – cos θ = 0
sin θ = cos θ
`sinθ/cosθ` = 1
`\implies` tan θ = tan 45°
∴ θ = 45°
Now sin4 θ + cos4 θ = sin4 45° + cos4 45°
= `(1/sqrt(2))^4 + (1/sqrt(2))^4`
= `1/4 + 1/4`
= `2/4`
sin4 θ + cos4 θ = `1/2`
APPEARS IN
RELATED QUESTIONS
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
If cot θ = `7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
If 3 cot θ = 2, find the value of `(4sin theta - 3 cos theta)/(2 sin theta + 6cos theta)`.
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
Find the value of x in the following :
`sqrt3 sin x = cos x`
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
Let tan9° = `(1 - sqrt((sqrt(5)k)/m))k` where k = `sqrt(5) + 1` then m is equal to ______.
