Question

Verify the identity.

sin2x/cosx + sinx = 2sinx


Solve for all values of x:

6cos2x-7cosx-3=0

If f(x)=cos1/2x-sin2x find the value of
f(pi)

Answer 1

the first identity is not correct

LS = sin2x/cosx + sinx
= 2sinxcosx/cosx + sinx
= 2sinx + sinx
= 3 sinx

You have RS = 2sinx

6cos2x-7cosx-3=0
You probably typed this incorrectly and really meant
6cos^2 x-7cosx-3=0
if so, let cosx = y, then our equation becomes
6y^2 - 7y - 3 = 0
(2y - 3)(3y + 1) = 0
y = 2/3 or y = -1/3

cosx = 2/3 or cosx = -1/3

for cosx = 2/3, x is in I or IV
x = 48.2 or 311.8°

for cosx = -1/3, x is in II or III
x = 109.5 or 250.5°

for the last one, sub in x = π