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Popular >

tan(arcsin(cos(x)))=-sqrt(3)

Solution

tan (arcsin (cos (x))) = - 3

Solution

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Solution steps

tan (arcsin (cos (x))) = - 3

Subtract

- 3

from both sides

tan (arcsin (cos (x))) + 3 = 0

Rewrite using trig identities

\frac{cos ( x )}{1 - cos ^{2} ( x )} + 3 = 0

Solve by substitution

cos (x) = - \frac{3}{2}

cos (x) = - \frac{3}{2} : x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Combine all the solutions

x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Popular Examples

4sin(x)cos(x)=-sqrt(3)

4 sin (x) cos (x) = - 3

solvefor t,x=3cos(t)solve for

t, x = 3 cos (t)

tan^2(θ)=-3/2 sec(θ),0<= θ<2pi

tan^{2} (θ) = - \frac{3}{2} sec (θ), 0 \leq θ < 2 π

5sin(x)+3cos(x)=0

5 sin (x) + 3 cos (x) = 0

sqrt(3)cos(x)csc(x)=2cos(x)

3 cos (x) csc (x) = 2 cos (x)

Frequently Asked Questions (FAQ)

What is the general solution for tan(arcsin(cos(x)))=-sqrt(3) ?
The general solution for tan(arcsin(cos(x)))=-sqrt(3) is x=(5pi)/6+2pin,x=(7pi)/6+2pin