If cos θ + sin θ =m, sec θ + cosec θ =n, what is m/n?

In ΔABC θ is an acute angle and tanθ is equal to three times of cotθ. Find the value of $$ {sin^{2}θ+cosec^{2}θ-{1\over 2}cot^{2}θ}$$.

Find the value of $$\left({1\over {sin 60°}} \right)^{2} + (cos 30°)^{2} \over(tan 45°)^{2}$$.

In the given figure BC=15 cm and Sin B=4/5.  then find out the value of AB?

If 1 + sin² A = 3 sin A cos A, then what are the possible values of tan A?

If  $$ {cosAcotA \over( 1 - sinA ) }=x $$ then the value of x is : 

If cosec 39°= x, the value of $$ {1\over {cosec^{2}{51°}}} +sin^{2} 39^{°}+tan^{2}{51^{°}}-{1\over {sin^{2}{51^{°}}}{Sec^{2}{39^{°}}}}$$ is-

If 0 ≤ θ ≤ 90⁰ and 4cos²θ - $$4{\sqrt { 3} \ }cosθ$$ + 3 = 0, then the value of θ is :