Advertisements
Advertisements
प्रश्न
(i)` (1-cos^2 theta )cosec^2theta = 1`
Advertisements
उत्तर
LHS= `(1-cos^2 theta) cosec^2 theta`
=`sin ^2 theta cosec^2 theta (∵ cos^2 theta + sin^2 theta =1)`
=`1/(cosec^2theta) ×cosec^2theta`
=1
Hence, LHS = RHS
APPEARS IN
संबंधित प्रश्न
`(1+tan^2A)/(1+cot^2A)` = ______.
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Without using the trigonometric table, prove that
cos 1°cos 2°cos 3° ....cos 180° = 0.
Without using trigonometric table, prove that
`cos^2 26° + cos 64° sin 26° + (tan 36°)/(cot 54°) = 2`
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
If tan θ = `7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ......[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` .......`[cos theta = 1/sectheta]`
Prove that `(1 + sin "B")/"cos B" + "cos B"/(1 + sin "B")` = 2 sec B
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
Simplify (1 + tan2θ)(1 – sinθ)(1 + sinθ)
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?
