Advertisements
Advertisements
Question
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Advertisements
Solution
LHS = `(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ)`
= `((1 + sinθ)(cosecθ + cotθ) - (1 - sinθ)(cosecθ - cotθ))/(cosec^2θ - cot^2θ)`
= `(cosecθ + cotθ + 1 + cosθ - cosecθ + cotθ + 1 - cosθ)/(1 + cot^2θ - cot^2θ)` (∵ `cosec^2θ = 1 + cot^2θ`)
= 2 + 2cotθ = 2(1 + cotθ)
APPEARS IN
RELATED QUESTIONS
Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Prove the following trigonometric identities.
`tan θ/(1 - cot θ) + cot θ/(1 - tan θ) = 1 + tan θ + cot θ`
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove that:
(cosec A – sin A) (sec A – cos A) sec2 A = tan A
If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?
Prove the following identity :
`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`
If cosθ = `5/13`, then find sinθ.
If tan α + cot α = 2, then tan20α + cot20α = ______.
