Advertisements
Advertisements
प्रश्न
If cos A + cos2 A = 1, then sin2 A + sin4 A =
विकल्प
−1
0
1
None of these
उत्तर
Given:
`cos A+cos^2 A=1`
`⇒ 1- cos^2 A= cos A`
So,
`sin^2 A+sin^4 A`
`= sin^2 A+sin^2 A sin^2 A`
`= sin^2 A+(1-cos^2 A)(1-cos^2 A)`
`=sin^2 A+cos A cos A`
`=sin^2 A+cos^2 A`
`=1`
APPEARS IN
संबंधित प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following trigonometric identities.
`tan^2 theta - sin^2 theta tan^2 theta sin^2 theta`
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Find the value of ( sin2 33° + sin2 57°).
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove that `(sin^2theta)/(cos theta) + cos theta` = sec θ
