Advertisements
Advertisements
Question
Select the correct option from the given alternatives:
The value of `costheta/(1 + sin theta)` is equal to .....
Options
`tan(theta/2 - pi/4)`
`tan(-pi/4 - theta/2)`
`tan(pi/4 - theta/2)`
`tan(pi/4 + theta/2)`
Advertisements
Solution
`tan(pi/4 - theta/2)`
Explanation:
`costheta/(1 + sintheta) = (cos^2 theta/2 - sin^2 theta/2)/(cos^2 theta/2 + sin^2 theta/2 + 2sin theta/2 cos theta/2)`
= `((cos theta/2 - sin theta/2)(cos theta/2 + sin theta/2))/((cos theta/2 + sin theta/2)^2`
= `(cos theta/2 - sin theta/2)/(cos theta/2 + sin theta/2)`
Dividing numerator and denominator by `cos theta/2`, we get
`costheta/(1 + sintheta) = (1 - tan theta/2)/(1 + tan theta/2) = tan(pi/4 - theta/2)`
APPEARS IN
RELATED QUESTIONS
Prove the following:
`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`
Prove the following:
`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`
If sin A = `(-5)/13, pi < "A" < (3pi)/2` and cos B = `3/5, (3pi)/2 < "B" < 2pi` find sin (A + B)
Select the correct option from the given alternatives :
If tan A – tan B = x and cot B – cot A = y, then cot (A – B) = _____
Select the correct option from the given alternatives :
The numerical value of tan 20° tan 80° cot 50° is equal to ______.
Prove the following:
3tan610° – 27 tan410° + 33tan210° = 1
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
cos (36° - A) cos (36° + A) + cos(54° + A) cos (54° - A) = ?
If f(x) = log (sec x + tan x), then `"f'"(π/4)` = ____________.
The value of sin 163° cos 347° + sin 167° sin 73° is ______
If A, B, C are the angles of ΔABC, then `tan A/2 tan B/2 + tan B/2 tan C/2 + tan C/2 tan A/2` = ______
If `(cos(x - y))/(cos(x + y)) = ("a" + "b")/("a" - "b")`, then cot x × cot y is equal to ______.
If equation tan θ + tan 2θ + tan θ tan 2θ = 1, θ = ______.
If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.
The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is ______.
If tan α = k cot β, then `(cos(α - β))/(cos(α + β))` is equal to ______.
If cos(81° + θ) = `sin(k/3 - θ)`, then k is equal to ______.
lf sin θ = cos θ, then the value of 2 tan2 θ + sin2 θ – 1 is equal to ______.
`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin 31^circ) - 8 sin^2 30^circ` is equal to ______.
If cos θ = `8/17` and θ lies in the 1st quadrant, then the value of cos(30° + θ) + cos(45° – θ) + cos(120° – θ) is ______.
If tan α, tan β are the roots of the equation x2 + px + q = 0 (p ≠ 0), then ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
If cos 2B = `(cos(A + C))/(cos(A - C))`, then tan A, tan B, tan C are in ______.
cos2 76° + cos2 16° – cos 76° cos 16° is equal to ______.
The value of cot 70° + 4 cos 70° is ______.
If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.
cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.
`1/3(sqrt(3) cos 23^circ - sin 23^circ)` is equal to ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
The value of tan 3A – tan 2A – tan A is ______.
