Advertisements
Advertisements
प्रश्न
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
Advertisements
उत्तर
LHS = `1/((cosA + sinA) - 1) + 1/((cosA + sinA) + 1)`
= `(cosA + sinA + 1 + cosA + sinA - 1)/((cosA + sinA)^2 -1)`
= `(2(cosA + sinA))/(cos^2A + sin^2A + 2cosAsinA - 1)`
= `(2(cosA + sinA))/(1 + 2cosAsinA - 1) = (cosA + sinA)/(cosAsinA)`
= `cosA/(cosAsinA) + sinA/(cosAsinA)`
= `1/sinA + 1/cosA`
= cosecA + secA
APPEARS IN
संबंधित प्रश्न
`1/((1+ sin θ)) + 1/((1 - sin θ)) = 2 sec^2 θ`
Show that none of the following is an identity:
`cos^2theta + cos theta = 1`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
If `sin theta = x , " write the value of cot "theta .`
Prove the following identity :
`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
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.
(sec θ + tan θ) . (sec θ – tan θ) = ?
Let α, β be such that π < α – β < 3π. If sin α + sin β = `-21/65` and cos α + cos β = `-27/65`, then the value of `cos (α - β)/2` is ______.
