Advertisements
Advertisements
Question
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Advertisements
Solution
L.H.S. = `1/(tan A + cot A)`
= `1/((sin A)/(cos A) + (cos A)/(sin A))`
= `1/((sin^2A + cos^2A)/(sin A cos A))`
= `1/(1/(sin A cos A))` ...(∵ sin2A + cos2A = 1)
= sin A cos A
= R.H.S.
APPEARS IN
RELATED QUESTIONS
`(1+tan^2A)/(1+cot^2A)` = ______.
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
If `m = (cos θ - sin θ)` and `n = (cos θ + sin θ)`, show that `sqrt(m/n) + sqrt(n/m) = 2/sqrt(1 - tan^2θ)`.
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
If x = a tan θ and y = b sec θ then
Prove that (1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B.
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
