Advertisements
Advertisements
Questions
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove that: tan θ + cot θ = sec θ cosec θ
Advertisements
Solution
L.H.S. = cot θ + tan θ
L.H.S. = `costheta/sintheta + sintheta/costheta`
L.H.S. = `(cos^2theta + sin^2theta)/(sintheta costheta)`
[cos2 θ + sin2 θ = 1]
L.H.S. = `1/(sintheta costheta)`
Use Reciprocal Identities:
The expression can be split into `(1/sin θ) xx (1/cos θ)`.
`1/sin θ` = cosec θ
`1/cos θ` = sec θ
L.H.S. = cosec θ.sec θ
L.H.S. = sec θ.cosec θ
∴ L.H.S. = R.H.S.
RELATED QUESTIONS
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Prove the following trigonometric identities.
`"cosec" theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
If `sin theta = x , " write the value of cot "theta .`
Prove the following identity :
`((1 + tan^2A)cotA)/(cosec^2A) = tanA`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
Show that tan4θ + tan2θ = sec4θ – sec2θ.
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
