Advertisements
Advertisements
Question
Prove that `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
Solution
L.H.S = `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)`
= `1/("cosec" theta)(cottheta + tantheta)` .....`[(because tan(90 - theta) = cot theta),(cot(90 - theta) = tantheta)]`
= sin θ (cot θ + tan θ)
= `sintheta ((costheta)/(sintheta) + (sintheta)/(costheta))`
= `sintheta ((cos^2theta + sin^2theta)/(sintheta costheta))`
= `sintheta (1/(sintheta costheta))` ......[∵ sin2θ + cos2θ = 1]
= `1/costheta`
= sec θ
= R.H.S
∴ `(tan(90 - theta) + cot(90 - theta))/("cosec" theta)` = sec θ
APPEARS IN
RELATED QUESTIONS
Prove that `cosA/(1+sinA) + tan A = secA`
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
Prove the following trigonometric identities.
`(tan^2 A)/(1 + tan^2 A) + (cot^2 A)/(1 + cot^2 A) = 1`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
Write the value of `( 1- sin ^2 theta ) sec^2 theta.`
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
(1 + sin A)(1 – sin A) is equal to ______.
