Home
Class 12
MATHS
If sin2A= lambda sin 2B prove that (tan...

If ` sin2A= lambda sin 2B` prove that `(tan(A+B)/tan(A-B))=(lambda+1)/(lambda-1)`

Text Solution

Verified by Experts

Given `sin2A=lambdasin 2B`
`rArr(Sin2A)/(sin2B)=(lambda)/(1)`
Applying componendo `&` dividendo,
`(sin2A+sin2B)/(sin2B-sin2A)=(lambda+1)/(1-lambda)`
`rArr(2sin((2A+2B)/(2))cos((2A-2B)/(2)))/(2cos((2B+2A)/(2))sin((2B-2A)/(2)))=(lambda+1)/(1-lambda)`
`rArr(sin(A+B)cos(A-B))/(cos(A+B)sin[-(A-B)])=(lambda+1)/(1-lambda)rArr(sin(A+B)cos(A-B))/(cos(A+B)x-sin(A-B))=(lambda+1)/(-(lambda-1))`
` rArr (sin(A+B)cos(A-B))/(cos(A+B)sin(A-B))=(lambda+1)/(lambda-1)rArr tan(A+B )cot(A-B)=(lambda+1)/(lambda-1)`
` rArr(tan(A+B))/(an(A-B))=(lambda+1)/(lambda-1)`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If sin2A=lambda sin2B prove that ((tan(A+B))/(tan(A-B)))=(lambda+1)/(lambda-1)

sin B=3sin(2A+B), prove that2tan A+tan(A+B)=0

If s in2A=lambda sin2B, then write the value of (lambda+1)/(lambda-1)

If2tan A=3tan B, then prove that sin(A+B)=5sin(A-B)

If cos A+cos B=(1)/(2) and sin A+sin B=(1)/(4) prove that: tan((A+B)/(2))=(1)/(2)

Prove that: If tan A=x tan B, prove that (sin(A-B))/(sin(A+B))=(x-1)/(x+1)

If tan(A+B)=3 tan A , prove that (a) sin(2A+B)=2sin B

Prove that :(tan A+tan B)/(tan A-tan B)=(sin(A+B))/(sin(A-B))

If sec theta+tan theta=lambda then prove that (lambda^2-1)/(lambda^2+1)=sin theta

A straight line L cuts the lines A B ,A Ca n dA D of a parallelogram A B C D at points B_1, C_1a n dD_1, respectively. If ( vec A B)_1,lambda_1 vec A B ,( vec A D)_1=lambda_2 vec A Da n d( vec A C)_1=lambda_3 vec A C , then prove that 1/(lambda_3)=1/(lambda_1)+1/(lambda_2) .