SOLUTION: Let cos beta =a .Find the expression for cos 2beta and sin 2beta in terms of a and hence confirm that

SOLUTION: Let cos beta =a .Find the expression for cos 2beta and sin 2beta in terms of a and hence confirm that - cos(square)2beta + sin(square)2beta = 1

Question 148438: Let cos beta =a .Find the expression for cos 2beta and sin 2beta in terms of a
and hence confirm that - cos(square)2beta + sin(square)2beta = 1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let cos(beta) =a/1; this implies that x = a and r=1
Therefore y = sqrt(1-a^2)
Therefore sin(beta)= [sqrt(1-a^2)]/r
-------------------------------------
Find the expression for cos(2beta) and sin(2beta) in terms of a:
cos(2beta) = cos^2(beta)-sin^2(beta
= a^2 - [(1-a^2)/r^2]
------------------------------------ ------
sin(2beta) = 2*sin(beta)*cos(beta)
= 2 * sqrt(1-a^2)/r]
--------------------------
and hence confirm that - cos^2(2beta) + sin^2(2beta) = 1
------------------
Subsitute to confirm that statement is true.
====================
Cheers,
Stan H.

RELATED QUESTIONS
find {{{cos(beta)}}} and {{{tan(beta)}}} if {{{cos(2beta)=2/3}}}, {{{3pi/2 <... (answered by Alan3354)

please help prove:... (answered by Alan3354)

Find the Exact value (No Decimals) of sin(105 degrees) using the sum or difference... (answered by Theo)

sin(A+B) = sin A cos B + cos A sin B cos(A+B) =... (answered by vleith)

Rewrite the expression as a simplified expression containing one term: cos (alpha +... (answered by jsmallt9)

find sin theta and sin beta in sin(a)cos((-sqrt 17)/9)+cos((sqrt 17/9))sin(b) (answered by ikleyn)

If cos beta = 0.6, find without using tables, the value of a) sin beta b) 1- cos^2... (answered by Alan3354)

A)write the equation cos(2 theta)-sin(theta)=0 in terms of sin (theta) B) Hence solve... (answered by stanbon)

Develop the formula for the tangent of the sum of angles in terms of the tangent of the... (answered by Fermat)