Advertisements
Advertisements
Question
`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`
Advertisements
Solution
LHS=`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta ))`
=`sqrt(((1+cos theta)^2)/((1-cos theta)(1+ cos theta))) + sqrt (((1-cos theta)^2)/((1+ cos theta) (1- cos theta))`
=`sqrt(((1+cos theta)^2)/((1-cos^2 theta))) + sqrt(((1-cos theta )^2)/((1-cos^2 theta))`
=` sqrt(((1+ cos theta)^2)/(sin^2 theta))+sqrt(((1-cos theta
)^2)/sin^2 theta)`
=`((1+cos theta))/(sin theta) + ((1-cos theta))/(sin theta)`
=`(1+ cos theta +1-cos theta)/sin theta`
=`2/sin theta`
= 2cos ecθ
= RHS
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(1+ secA)/sec A = (sin^2A)/(1-cosA)`
[Hint : Simplify LHS and RHS separately.]
Prove the following trigonometric identities.
(1 + cot A − cosec A) (1 + tan A + sec A) = 2
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove the following identities:
`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
`(1 + cot^2 theta ) sin^2 theta =1`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Write the value of `(1 + cot^2 theta ) sin^2 theta`.
If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`
Write the value of cos1° cos 2°........cos180° .
If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.
Write True' or False' and justify your answer the following :
The value of \[\sin \theta\] is \[x + \frac{1}{x}\] where 'x' is a positive real number .
\[\frac{x^2 - 1}{2x}\] is equal to
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
Prove that `"cot A"/(1 - cot"A") + "tan A"/(1 - tan "A")` = – 1
Prove that (1 – cos2A) . sec2B + tan2B(1 – sin2A) = sin2A + tan2B
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
