Advertisements
Advertisements
प्रश्न
Prove that `cosA/(1+sinA) + tan A = secA`
Advertisements
उत्तर
L.H.S `cosA/(1+sinA) + tan A`
`= (cos A(1-sinA))/((1+sinA)(1-sinA)) + sinA/cosA`
`= (cosA - sinAcosA)/(1-sin^2A) + sinA/cosA`
`= (cosA - sinAcosA)/cos^2A + sinA/cosA`
`= 1/cosA - sinA/cosA + sinA/cosA`
`= 1/cosA`
= secA
=R.H.S
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`
`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`
`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
Prove the following identities:
`(1 + cos theta - sin^2 theta )/(sin theta (1 + cos theta)) = cot theta`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
Write the value of`(tan^2 theta - sec^2 theta)/(cot^2 theta - cosec^2 theta)`
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Eliminate θ if x = r cosθ and y = r sinθ.
