Advertisements
Advertisements
Question
if `3 cos theta = 1`, find the value of `(6 sin^2 theta + tan^2 theta)/(4 cos theta)`
Solution
Given `3 cos theta = 1`
We have to find the value of the expression `(6 sin^2 theta + tan^2 theta)/(4 cos theta)`
We have
`3 cos theta = 1`
`=> cos theta = 1/3`
`sin theta = sqrt(1 - cos^2 theta) = sqrt(1- (1/3)^3) = sqrt8/3`
`tan theta = sin theta/cos theta = (sqrt8/3)/(1/3) = sqrt8`
Therefore,
`(6 sin^2 theta + tan^2 theta)/(4 cos theta) = (6 xx (sqrt8/3)^2 + (sqrt8)^2)/(4 xx 1/3)`
= 10
Hence, the value of the expression is 10.
APPEARS IN
RELATED QUESTIONS
`\text{Evaluate }\frac{\tan 65^\circ }{\cot 25^\circ}`
Without using trigonometric tables, evaluate the following:
`( i)\frac{\cos37^\text{o}}{\sin53^\text{o}}\text{ }(ii)\frac{\sin41^\text{o}}{\cos 49^\text{o}}(iii)\frac{\sin30^\text{o}17'}{\cos59^\text{o}\43'}`
If A, B, C are the interior angles of a triangle ABC, prove that `\tan \frac{B+C}{2}=\cot \frac{A}{2}`
Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
Evaluate.
sin235° + sin255°
Express the following in terms of angles between 0° and 45°:
cosec68° + cot72°
A triangle ABC is right angles at B; find the value of`(secA.cosecC - tanA.cotC)/sinB`
Prove that:
`(cos(90^circ - theta)costheta)/cottheta = 1 - cos^2theta`
Use tables to find sine of 21°
Prove that:
sin (28° + A) = cos (62° – A)
If 0° < A < 90°; find A, if `(cos A )/(1 - sin A) + (cos A)/(1 + sin A) = 4`
What is the maximum value of \[\frac{1}{\sec \theta}\]
If \[\frac{{cosec}^2 \theta - \sec^2 \theta}{{cosec}^2 \theta + \sec^2 \theta}\] write the value of \[\frac{1 - \cos^2 \theta}{2 - \sin^2 \theta}\]
If A + B = 90° and \[\tan A = \frac{3}{4}\]\[\tan A = \frac{3}{4}\] what is cot B?
If \[\tan A = \frac{5}{12}\] \[\tan A = \frac{5}{12}\] find the value of (sin A + cos A) sec A.
If x sin (90° − θ) cot (90° − θ) = cos (90° − θ), then x =
In the following figure the value of cos ϕ is
Find the value of the following:
tan 15° tan 30° tan 45° tan 60° tan 75°
In ∆ABC, cos C = `12/13` and BC = 24, then AC = ?
