If cos A + cos^2A = 1, then sin^2A + sin^4A = ?

If cos A + cos²A = 1, then sin²A + sin⁴A = ?

Sum

cos A + cos²A = 1 ...[Given]

∴ cos A = 1 – cos²A

∴ cos A = sin²A ...`[(∵ sin^2A + cos^2A = 1),(∴ 1 - cos^2A = sin^2A)]`

∴ cos²A = sin⁴A ...[Squaring both the sides]

∴ 1 – sin²A = sin⁴A

∴ 1 = sin⁴A + sin²A

∴ sin²A + sin⁴A = 1

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Chapter 6 Trigonometry
Exercise | Q 5. 2.

Prove the following trigonometric identities.

`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`

Prove the following trigonometric identity:

`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`

Prove the following trigonometric identities.

`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`

Prove the following trigonometric identities.

(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A

Prove the following trigonometric identities.

if cos A + cos²A = 1, prove that sin² A + sin⁴ A = 1

Prove the following identities:

`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`

Prove the following identities:

`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`

Prove the following identities:

`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta )/(cos theta)`

If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?

Write True' or False' and justify your answer the following :

The value of \[\cos^2 23 - \sin^2 67\] is positive .