If cos theta=(cos alpha-cos beta)/(1-cos...

If `cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta),`prove that `tan theta/2=+-tan alpha/2 cot beta/2.`

Text Solution

AI Generated Solution

Topper's Solved these Questions

TRIGONOMETRIC FUNCTIONS AND IDENTITIES
ARIHANT MATHS ENGLISH|Exercise Solved Examples : Single Option Correct Type Questions|2 Videos
TRIGONOMETRIC FUNCTIONS AND IDENTITIES
ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|10 Videos
TRIGONOMETRIC EQUATIONS AND INEQUATIONS
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos
VECTOR ALGEBRA
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

If cos theta=(cos alpha cos beta)/(1-sin alpha sin beta), prove that one value of (tan) theta/2=(tan alpha/2-tan beta/2)/(1-t a n alpha/2 tan beta/2).

If cos theta=(cos alpha cos beta)/(1-sin alpha sin beta), prove that one value of tan (theta/2)=(tan (alpha/2)-tan (beta/2))/(1-tan (alpha/2) tan (beta/2)).

Prove that (cos^2 alpha - cos^2 beta)/(cos^2 alpha*cos^2 beta) = tan^2 beta - tan^2 alpha

Show that cos^(-1) ((cos alpha+cos beta)/(1+cosalpha cosbeta))=2 tan^(-1)(tan (alpha/2) tan (beta/2))

If sin (theta + alpha ) = cos ( theta + alpha), prove that tan theta =(1- tan alpha )/(1 + tan alpha )

If sin alpha sin beta - cos alpha cos beta + 1=0, then the value of 1+cot alpha tan beta is

cos 2 alpha =(3 cos 2 beta -1)/( 3-cos 2 beta), then tan alpha=

If sin alpha.sinbeta - cos alpha.cos beta+1=0 , then find the value of cot alpha.tan beta .

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

Under rotation of axes through theta , x cosalpha + ysinalpha=P changes to Xcos beta + Y sin beta=P then . (a) cos beta = cos (alpha - theta) (b) cos alpha= cos( beta - theta) (c) sin beta = sin (alpha - theta) (d) sin alpha = sin ( beta - theta)

ARIHANT MATHS ENGLISH-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)

If cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta),prove that ta...
Text Solution
|
Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...
Text Solution
|
Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...
Text Solution
|
The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...
Text Solution
|
Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta ...
Text Solution
|
The number of all possible values of theta, where 0 lt theta lt pi, fo...
Text Solution
|
For 0 lt theta lt pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+(...
Text Solution
|
If sin^ 4 x/2+cos^4 x/3 =1/5 then
Text Solution
|
Let theta in (0,pi/4) and t1=(tan theta)^(tan theta), t2=(tan theta)^(...
Text Solution
|
cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...
Text Solution
|
If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...
Text Solution
|
Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...
Text Solution
|
The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...
Text Solution
|
If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...
Text Solution
|
If A = sin^2x + cos^4 x, then for all real x :
Text Solution
|
Let cos(alpha+beta)""=4/5 and let sin (alpha+beta)""=5/(13) where 0lt=...
Text Solution
|
If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...
Text Solution
|
A triangular park is enclosed on two sides by a fence and on the third...
Text Solution
|
If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is
Text Solution
|
In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...
Text Solution
|