Advertisements
Advertisements
Question
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
Advertisements
Solution
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
RELATED QUESTIONS
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
if `cosec theta - sin theta = a^3`, `sec theta - cos theta = b^3` prove that `a^2 b^2 (a^2 + b^2) = 1`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
If x sin3θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ , then show that x2 + y2 = 1.
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
Without using a trigonometric table, prove that
`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.
Prove that `(sin^2θ)/(cos θ) + cos θ = sec θ`.
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
