Advertisements
Advertisements
प्रश्न
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
उत्तर
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^@73^@)`
`(= [sin(90^@ - 27^@)]^2+sin^2 27^@)/([cos(90^@ - 73^@)]^2 + cos^2 73^@)`
`= ([cos27^@]^2 + sin^2 27^@)/([sin 73^@]^2 + cos^2 73^@)`
`= (cos^2 27^@ + sin^2 27^@)/(sin^2 73^@+ cos^2 73^@)`
= 1/1 (As sin2A + cos2A = 1)
= 1
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m2 – n2 = a2 – b2
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
`(sec^2 theta-1) cot ^2 theta=1`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Prove the following identity :
`(1 + cotA + tanA)(sinA - cosA) = secA/(cosec^2A) - (cosecA)/sec^2A`
Prove that :
2(sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) + 1 = 0
Prove that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
Eliminate θ if x = r cosθ and y = r sinθ.
