Advertisements
Advertisements
Question
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Advertisements
Solution
L.H.S
= `sqrt((1+sinA)/(1-sinA))`
= `sqrt(((1+sinA)(1+sinA))/((1-sinA)(1+sinA))`
= `(1+sinA)/(sqrt(1-sin^2A))`
= `(1+sinA)/sqrt(cos^2A)`
= `(1+sinA)/cosA`
= secA + tan A
= `1/cos A + sin A/cos A`
= R.H.S
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
`tan theta + 1/tan theta = sec theta cosec theta`
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
The value of sin2 29° + sin2 61° is
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
Prove that `(1 + sintheta)/(1 - sin theta)` = (sec θ + tan θ)2
