Advertisements
Advertisements
Question
`(cos ec^theta + cot theta )/( cos ec theta - cot theta ) = (cosec theta + cot theta )^2 = 1+2 cot^2 theta + 2cosec theta cot theta`
Solution
Here, `( cosec theta + cot theta )/( cosec theta - cot theta)`
= `((cosec theta + cot theta) ( cosec theta + cot theta ))/(( cosec theta - cot theta ) ( cosec theta + cot theta))`
=` ((cosec theta + cot theta)^2)/(( cosec ^2 theta - cot^2 theta))`
=`((cosec theta + cot theta )^2) /1`
=`(cosec theta + cot theta )^2`
Again , `( cosec theta + cot theta )^2`
= ` cosec^2 theta + cot^2 theta + 2 cosec theta cot theta `
=` 1+cot^2 theta + cot^2 theta + 2 cosec theta cot theta (∵ cosec^2 theta - cot^2 theta =1)`
=` 1+2 cot^2 theta + 2 cosec theta cot theta `
APPEARS IN
RELATED QUESTIONS
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
If cos θ + cot θ = m and cosec θ – cot θ = n, prove that mn = 1
Prove the following identities:
`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
What is the value of 9cot2 θ − 9cosec2 θ?
(sec A + tan A) (1 − sin A) = ______.
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Prove that `1/("cosec" theta - cot theta)` = cosec θ + cot θ
If cos A + cos2A = 1, then sin2A + sin4 A = ?
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
