IS `(cos A)/( sin A) ` equal to cot A ?

Is (sin A )/( cos A) equal to tan A ?

Prove that (cosec A - sin A ) (sec A -cos A) = ( 1)/( tan A +cot A)

(cos 10^0+sin 10^0)/(cos 10^0-sin 10^0) is equal to a. tan55^0 b. cos 55^0 c. -tan35^0 d. -cot35^0

Prove that (cos 7x + cos 5x)/( sin 7x - sin 5x) = cot x

cos^2 48^0-sin^2 12^0 is equal to

alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos ^2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 sin alpha + sin beta + sin gamma can be equal to

alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos 2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 cos alpha + cos beta + cos gamma can be equal to

Given that sin (A+ B) = sin A cos B + cos A sin B , find the value of sin 75° .

Prove that (sin A +cosec A) ^(2) +(cos A +sec A) ^(2) =7+ tan ^(2) A +cot ^(2) A

Find the number of solution of the equations |cot x|= cot x +(1)/(sin x), when x in [0,2pi]