Advertisements
Advertisements
Question
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
Solution
`cosec ^2 (90°- theta )- tan^2 theta `
=` sec^2 theta - tan^2 theta`
= 1
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`
Prove the following identities:
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
If `sec theta = x ,"write the value of tan" theta`.
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
Show that tan4θ + tan2θ = sec4θ – sec2θ.
Prove the following trigonometry identity:
(sinθ + cosθ)(cosecθ – secθ) = cosecθ.secθ – 2 tanθ
