Advertisements
Advertisements
प्रश्न
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Advertisements
उत्तर
LHS = `sqrt((1 + sin A)/(1 - sin A))`
= `sqrt((1 + sin A)/(1 - sin A) xx (1 + sin A)/(1 + sin A)`
= `sqrt((1 + sin A)^2/(1 - sin^2 A))`
= `sqrt((1 + sin A)^2/cos^2 A)`
= `(1 + sin A)/cos A`
= sec A + tan A = RHS
संबंधित प्रश्न
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Prove that:
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.
What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?
Write True' or False' and justify your answer the following:
\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Choose the correct alternative:
1 + tan2 θ = ?
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.
Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
= `square` – cos2A ...[sin2A = 1 – cos2A]
= `square`
= R.H.S.
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
