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:
`(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 cos (A – B)
If tan A = `5/6, tan "B" = 1/11`, prove that A + B = `pi/4`
Select the correct option from the given alternatives :
The value of sin(n + 1) A sin (n + 2) A + cos(n + 1) A cos(n + 2) A is equal to
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:
If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`
Prove the following:
`(2cos2"A" + 1)/(2cos2"A" - 1)` = tan(60° + A) tan(60° − A)
Prove the following:
tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A
Prove the following:
`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx
`(cos 25^circ + sin 25^circ)/(cos 25^circ - sin 25^circ)` = ?
tan A +2 tan 2A + 4 tan 4A + 8 cot 8A = ?
\[\frac{1 - \text{sin} \theta + \text{cos} \theta}{1 - \text{sin} \theta - \text{cos} \theta}\] = ?
If x cos θ + y sin θ = 5, x sin θ − y cos θ = 3, then the value of x2 + y2 = ____________.
The imaginary part of `1/(1 - sintheta + icostheta)` is equal to ______
If sin A + cos A = `sqrt(2)`, then the value of cos2 A is ______.
The value of cos 15° is ______.
If `0 < β < α < π/4, cos (α + β) = 3/5` and cos (α – β) = `4/5`, then sin 2α is equal to ______.
The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is ______.
If cos(A – B) = `3/5` and tan A tan B = 2, then ______.
tan 100° + tan 125° + tan 100° tan 125° = ______.
If `π/2 < α < π, π < β < (3π)/2`; sin α = `15/17` and tan β = `12/5`, then the value of sin(β – α) is ______.
If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.
sin 4θ can be written as ______.
cos2 76° + cos2 16° – cos 76° cos 16° is equal to ______.
The value of cot 70° + 4 cos 70° is ______.
If A, B, C, D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to ______.
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 ______.
tan 57° – tan 12° – tan 57° tan 12° is equal to ______.
The value of (cos α + cos β)2 + (sin α + sin β)2 is ______.
cos2 x + cos2 y – 2 cos x cos y cos (x + y) is equal to ______.
