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Trigonometric equations questions





Question 1.
Find the Principal solutions of the below trigonometric equations
a. $\sin (x)= \frac {\sqrt 3}{2}$
b. $\cos (x) =- \frac {1}{\sqrt 2}$
c. tan x=-1

Find the general solution of the equation
Question 2.
$ \sin (\frac {\theta }{2}) =-1$

Question 3.
$ \cos (3\theta) = - \frac {1}{2} $

Question 4.
$5 \cos^2 (\theta) + 7 \sin^2 (\theta) - 6 = 0$

Question 5.
$ \sin^2 (x) = \frac {3}{4}$

Question 6.
$ \sqrt 3 \cos (\theta) + \sin (\theta) = \sqrt 2$

Question 7.
Find the general solution of the equation
$(\sqrt 3 - 1) \cos (\theta) + (\sqrt 3 + 1) \sin (\theta) = 2$

Question 8.
Solve sin (2x) - sin (4x) + sin (6x) = 0.

Question 9.
$4 \cos^2 (x) \sin (x) - 2 \sin^2 (x) = 3 \sin (x)$

Question 10.
Determine all the values of b for which the equation $\cos^4 (x) - (b+2) \cos^2 (x) -(b+3)=0$ possesses solution . Find the solutions also

Question 11.
Solve the below equation
$\tan (5x) = \cot (2x)$

Question 12.
Solve the below equation
$\sec (4x) - \sec(2x) =2$



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