Advertisements
Advertisements
प्रश्न
if `sqrt3 tan theta = 3 sin theta` find the value of `sin^2 theta - cos^2 theta`
उत्तर
Given `sqrt3 tan theta = 3 sin theta`
We have to find the value of `sin^2 theta -cos^2 theta`
`sqrt3 tan theta = 3 sin theta`
`=> sqrt3 sin theta/cos theta = 3 sin theta`
`=> cos theta = sqrt3/3`
Therefore
`sin^2 theta - cos^2 theta = 1 - cos^2 theta - cos^2 theta` (since `sin^2 theta + cos^2 theta = 1`)
`= 1 - 2 cos^2 theta`
`= 1 - 2 xx (1/sqrt3)^2`
`= 1/3`
Hence, the value of the expression is 1/3
APPEARS IN
संबंधित प्रश्न
If the angle θ = -60° , find the value of sinθ .
if `cot theta = 1/sqrt3` find the value of `(1 - cos^2 theta)/(2 - sin^2 theta)`
Evaluate.
`cot54^@/(tan36^@)+tan20^@/(cot70^@)-2`
Express the following in terms of angles between 0° and 45°:
cosec68° + cot72°
Evaluate:
`3 sin72^circ/(cos18^circ) - sec32^circ/(cosec58^circ)`
Find the value of x, if tan x = `(tan60^circ - tan30^circ)/(1 + tan60^circ tan30^circ)`
Prove that:
sec (70° – θ) = cosec (20° + θ)
If 4 cos2 A – 3 = 0 and 0° ≤ A ≤ 90°, then prove that sin 3 A = 3 sin A – 4 sin3 A
If 3 cot θ = 4, find the value of \[\frac{4 \cos \theta - \sin \theta}{2 \cos \theta + \sin \theta}\]
If A and B are complementary angles, then
If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ −\[\sqrt{3} \tan 3\theta\] is equal to
If \[\cos \theta = \frac{2}{3}\] then 2 sec2 θ + 2 tan2 θ − 7 is equal to
Prove that:
\[\left( \frac{\sin49^\circ}{\cos41^\circ} \right)^2 + \left( \frac{\cos41^\circ}{\sin49^\circ} \right)^2 = 2\]
Find the sine ratio of θ in standard position whose terminal arm passes through (4,3)
The value of tan 72° tan 18° is
In ∆ABC, `sqrt(2)` AC = BC, sin A = 1, sin2A + sin2B + sin2C = 2, then ∠A = ? , ∠B = ?, ∠C = ?
2(sin6 θ + cos6 θ) – 3(sin4 θ + cos4 θ) is equal to ______.
If x and y are complementary angles, then ______.
The value of the expression (cos2 23° – sin2 67°) is positive.
