Advertisements
Advertisements
प्रश्न
Prove that `(cos^2θ)/(sinθ) + sin θ = "cosec" θ`.
Advertisements
उत्तर
L.H.S. = `(cos^2θ)/(sinθ) + sin θ`
= `(cos^2θ + sin^2θ)/(sin θ)`
= `1/(sin θ)` ...[∵ sin2θ + cos2θ = 1]
= cosec θ
= R.H.S.
∴ `(cos^2θ)/(sin θ) + sin θ = "cosec" θ`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 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.
if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
If x = a cos3θ and y = b sin3θ, prove that `(x/a)^(2/3) + (y/b)^(2/3) = 1`.
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
(sec θ + tan θ) . (sec θ – tan θ) = ?
Prove that cot2θ – tan2θ = cosec2θ – sec2θ.
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
