Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
Advertisements
उत्तर
`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`
`(1 + cosA)/sinA + sinA/(1 + cosA)`
= `((1 + cosA)^2 + sin^2A)/(sinA(1 + cosA))`
= `(1 + 2cosA + cos^2A + sin^2A)/(sinA(1 + cosA))`
= `(2 + 2cosA)/(sinA(1 + cosA))`
= `(2(1 + cosA))/(sinA(1 + cosA)` [`sin^2A + cos^2A = 1`]
= 2 cosec A
APPEARS IN
संबंधित प्रश्न
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
If acosθ – bsinθ = c, prove that asinθ + bcosθ = `\pm \sqrt{a^{2}+b^{2}-c^{2}`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
`(sec^2 theta-1) cot ^2 theta=1`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
