Originally Posted by
mrjameslat Ok I don't understand how to do these 3 types of questions.
Please help me understand how to do them. Thanks for your time.
1. Verify the identity (Can only change one side, and end result must equal each other)
cos^3Xsin^2X=(sin^2X-sin^4X)cosX
left side ... cosx(cos^2x sin^2x) = cosx[(1 - sin^2x)sin^2x] = cosx(sin^2x - sin^4x)
2. Sole the equation.
4cosX=1+2cosX
subtract 2cosx from both sides ...
2cosx = 1
cosx = 1/2 ... x = pi/3, x = 5pi/3
3. Find the exact values of the sine, cosine, and tangent of the angle by using the sum or difference formula.
345 degrees = 300 degrees + 45 degrees
use the sum/difference identities ...
cos(a+b) = cosa cosb - sina sinb
sin(a+b) = sina cosb + cosa sinb
tan(a+b) = (tana + tanb)/(1 - tana tanb)