Advertisements
Advertisements
Question
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
Advertisements
Solution
`(1+ tan^2 theta )(1+ sin theta )(1- sintheta)`
=` sec^2 theta (1- sin^2 theta )`
=`1/ cos^2 theta xx cos^2 theta`
= 1
APPEARS IN
RELATED QUESTIONS
Express the ratios cos A, tan A and sec A in terms of sin A.
9 sec2 A − 9 tan2 A = ______.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
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:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
`sec theta (1- sin theta )( sec theta + tan theta )=1`
`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
If sec θ + tan θ = x, then sec θ =
The value of sin2 29° + sin2 61° is
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Prove that cosec2 (90° - θ) + cot2 (90° - θ) = 1 + 2 tan2 θ.
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
If `(cos alpha)/(cos beta)` = m and `(cos alpha)/(sin beta)` = n, then prove that (m2 + n2) cos2 β = n2
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
sin2θ + sin2(90 – θ) = ?
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
