Advertisements
Advertisements
Question
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
Advertisements
Solution
L.H.S. = `(1 + sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A)`
= `((1 + sin A)(cosec A + cot A) - (1 - sin A)(cosec A - cot A))/((cosec A - cot A)(cosec A + cot A))`
= `(cosec A + cot A + sin A cosec A + sin A cot A - cosec A + cot A + sin A cosec A - sin A cos A)/(cosec^2A - cot^2A)`
= 2 cot A + 2 sin A cosec A
= 2 cot A + 2 `1/(cosec A) xx cosec A`
= 2 (cot A + 1)
Hence proved.
APPEARS IN
RELATED QUESTIONS
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
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.
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ.
Prove that `(1 + sin θ)/(1 - sin θ) = (sec θ + tan θ)^2`.
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
