Advertisements
Advertisements
Question
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Advertisements
Solution
`(1 - cosA)/sinA + sinA/(1 - cosA)`
= `((1 - cosA)^2 + sin^2A)/(sinA(1 - cosA))`
= `(1 + cos^2A - 2cosA + sin^2A)/(sinA(1 - cosA))`
= `(2 - 2cosA)/(sinA(1 - cosA))`
= `(2(1 - cosA))/(sinA(1 - cosA))`
= 2 cosec A
RELATED QUESTIONS
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
Write the value of ` sec^2 theta ( 1+ sintheta )(1- sintheta).`
Write True' or False' and justify your answer the following :
The value of sin θ+cos θ is always greater than 1 .
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
Choose the correct alternative:
Which is not correct formula?
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
