Advertisements
Advertisements
Question
if `cot theta = sqrt3` find the value of `(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta)`
Solution
`Given `cot theta = sqrt3`
We have to find the value of the expression `(cosec^2 theta = cot^2 theta)/(cosec^2 theta - sec^2 theta)`
We know that
`cot theta = sqrt3 => cot^2 theta = 3`
`cosec^2 theta =1 + cot^2 theta = 1 + (sqrt3)^2 = 4`
`sec^2 theta = 1/cos^2 theta = 1/(1 - sin^2 theta) = 1/(1 - 1/cosec^2 theta) = 1/(1 - 1/4) = 4/3`
Therefore
`(cosec^2 theta + cot^2 theta)/(cosec^2 theta - sec^2 theta) = (4 + 3)/(4 - 4/3)`
`= 21/8`
Hence, the value of the given expression is 21/8
APPEARS IN
RELATED QUESTIONS
If the angle θ = -60° , find the value of sinθ .
If sec 4A = cosec (A− 20°), where 4A is an acute angle, find the value of A.
Without using trigonometric tables evaluate:
`(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@`
Solve.
`sec75/(cosec15)`
For triangle ABC, show that : `tan (B + C)/2 = cot A/2`
Use tables to find sine of 10° 20' + 20° 45'
Use tables to find the acute angle θ, if the value of sin θ is 0.3827
If 0° < A < 90°; find A, if `(cos A )/(1 - sin A) + (cos A)/(1 + sin A) = 4`
If \[\cos \theta = \frac{2}{3}\] find the value of \[\frac{\sec \theta - 1}{\sec \theta + 1}\]
Write the value of tan 10° tan 15° tan 75° tan 80°?
If θ is an acute angle such that \[\cos \theta = \frac{3}{5}, \text{ then } \frac{\sin \theta \tan \theta - 1}{2 \tan^2 \theta} =\] \[\cos \theta = \frac{3}{5}, \text{ then } \frac{\sin \theta \tan \theta - 1}{2 \tan^2 \theta} =\]
If tan2 45° − cos2 30° = x sin 45° cos 45°, then x =
If x tan 45° cos 60° = sin 60° cot 60°, then x is equal to
The value of
Prove that:
\[\left( \frac{\sin49^\circ}{\cos41^\circ} \right)^2 + \left( \frac{\cos41^\circ}{\sin49^\circ} \right)^2 = 2\]
Prove that:
(sin θ + 1 + cos θ) (sin θ − 1 + cos θ) . sec θ cosec θ = 2
A, B and C are interior angles of a triangle ABC. Show that
sin `(("B"+"C")/2) = cos "A"/2`
Evaluate: `(cot^2 41°)/(tan^2 49°) - 2 (sin^2 75°)/(cos^2 15°)`
If tan θ = cot 37°, then the value of θ is
`(sin 75^circ)/(cos 15^circ)` = ?
