Advertisements
Advertisements
प्रश्न
Prove the following identities:
(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1
Prove that:
(cosec A − sin A) (sec A – cos A) (tan A + cot A) = 1
Advertisements
उत्तर
L.H.S. = (cosec A – sin A) (sec A – cos A) (tan A + cot A)
= `(1/sinA - sinA)(1/cosA - cosA)(1/tanA + tanA)`
= `((1 - sin^2A)/sinA)((1 - cos^2A)/cosA)(sinA/cosA + cosA/sinA)`
= `(cos^2A/sinA)(sin^2A/cosA)((sin^2A + cos^2A)/(sinA.cosA))`
= `(cos^2A/sinA)(sin^2A/cosA)((1)/(sinA.cosA))`
= `(cos^2A sin^2A)/((sinA .cosA)(sinA.cosA ))`
= `(cos^2A sin^2A)/(sin^2A cos^2A)`
= 1
= R.H.S.
संबंधित प्रश्न
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
Prove the following:
`sintheta/(1 + cos theta) + (1 + cos theta)/sintheta` = 2cosecθ
Prove the following that:
`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ
