Advertisements
Advertisements
प्रश्न
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
Advertisements
उत्तर
L.H.S. = `(sin θ + "cosec" θ)/(sin θ)`
= `(sin θ)/(sin θ) + ("cosec" θ)/(sin θ)`
= 1 + cosec θ × cosec θ ...`[∵ "cosec" θ = 1/(sin θ)]`
= 1 + cosec2θ
= 1 + 1 + cot2θ ...[∵ 1 + cot2θ = cosec2θ]
= 2 + cot2θ
= R.H.S.
∴ `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
Write the value of tan1° tan 2° ........ tan 89° .
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
What is the value of 9cot2 θ − 9cosec2 θ?
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ) + cos2 θ.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
If 5x = sec θ and `5/x` = tan θ, then `x^2 - 1/x^2` is equal to
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
