Advertisements
Advertisements
प्रश्न
If cos A + cos2A = 1, then sin2A + sin4A = ?
Advertisements
उत्तर
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
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
Write the value of tan10° tan 20° tan 70° tan 80° .
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
cos4 A − sin4 A is equal to ______.
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.
Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.
Activity:
L.H.S. = `square`
= `cos^2θ xx square` ...`[1 + tan^2θ = square]`
= `(cos θ xx square)^2`
= 12
= 1
= R.H.S.
Prove that `(cot A)/(1 - tan A) + (tan A)/(1 - cot A) = 1 + tan A + cot A = sec A . "cosec" A + 1`.
If cosec A – sin A = p and sec A – cos A = q, then prove that `(p^2q)^(2/3) + (pq^2)^(2/3) = 1`.
