# Trigonometry Problems - sin, cos, tan, cot: Difficult Problems with Solutions

Problem 1
Solve the trigonometric equation: $$tan3x={\frac{1}{tan2x}}$$.
Problem 2
Prove the trigonometric identity: $$tan4\alpha-{\frac{1}{cos4\alpha}}={\frac{sin2\alpha-cos2\alpha}{sin2\alpha+cos2\alpha}}$$
Problem 3
Solve the trigonometric equation: $$sin^2x+cos2x={\frac{1}{4}}$$
Problem 4
$$sin5x=cos7x$$
Problem 5
Solve the equation $$\cos^2x+\sin x={\frac{5}{4}}$$
Problem 6
Solve the trigonometric equation:
$$sin^2+3sin x cos x+7cos^2x=6$$
Problem 7
Solve the trigonometric equation
$$sin3x cos x=sin7x cos5x$$.
Problem 8
Solve the trigonometric equation: $$3cos x+2\sqrt{3sin x}={\frac{9}{2}}$$.
Problem 9
Solve the trigonometric equation: $$sin(x)cos(x)cos(2x)={\frac{1}{8}}$$.
Problem 10
Solve the trigonometric equation: $$sin^4x+cos^4x={\frac{5}{8}}$$.

Problem 11
Solve $$sin x-cos x=0$$.
Problem 12
Solve the trigonometric equation: $$sin x+cos x=\sqrt{2}sin5x$$.
Problem 13
Solve the equation: $$sin3x=cos2x$$.

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