Advertisements
Advertisements
Question
\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to
Options
sec2 A
−1
cot2 A
tan2 A
Advertisements
Solution
Given:
`(1+tan^2 A)/(1+cot^2 A)`
`= (1+sin^2 A/cos^2 A)/(1+cos^2/sin^2A)`
`=(cos^2 A+sin^2 A/cos^2 A)/(sin^2 A+cos^2 A/sin^2A)`
`=(1/cos^2 A)/(1/sin^2A)`
`=sin^2 A/cos^2 A`
`= tan^2 A`
APPEARS IN
RELATED QUESTIONS
If (secA + tanA)(secB + tanB)(secC + tanC) = (secA – tanA)(secB – tanB)(secC – tanC) prove that each of the side is equal to ±1. We have,
(secA + tanA) (1 − sinA) = ______.
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
Prove that:
`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove the following identity :
`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`
Prove the following identity :
`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
If cosθ = `5/13`, then find sinθ.
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
Prove that `(cos(90 - "A"))/(sin "A") = (sin(90 - "A"))/(cos "A")`
