In a ∆ABC, if ∠A = 45^o, ∠B = 60^o and ∠C = 75^o, then the ratio of sides is ______.

In a ΔABC if a = 5, b = 6 and c = 5, then ∠B is ______.

sin⁶\(\theta\) + cos⁶\(\theta\) + 3 sin²\(\theta\) cos²\(\theta\) is equal to ______.

If tan \(\theta={\alpha\over \alpha+1}\) and tan \(\phi ={1\over 2\alpha+1}\) , then (A+ B) is equal to ______.

If A, B, C are in A.P. then \({sinA-sinC\over cosC-cosA}\) is equal to ______.

In \(\triangle \)ABC, if a=3, b=5 and sin A=\(\frac { 3 }{ 5 } \), find \(\angle \) B.

Prove that \(cos\left( \frac { 3\pi }{ 4 } +x \right) -cos\left( \frac { 3\pi }{ 4 } -x \right) =-\sqrt { 2 } sinx.\)

Find the degree measure corresponding to following radian measures.
(-3)^c

Convert the following into radians.
520^o

Find the values of sin 75⁰

If \(\tan A=\frac14\) and \(\tan B=\frac15\), then find the value of \(\tan(A+B)\)

If sin A=\(\frac { 3 }{ 5 } \), 0\(\frac { \pi }{ 2 } \) and cos B=\(-\frac { 12 }{ 13 } \), \(\pi \) \(\frac { 3\pi }{ 2 } \) , then find the following.
cos (A + B)

Prove the following: tan x = \({4\tan x(1-\tan^2 \ x)\over 1-6\ \tan^2 \ x+\tan^4 \ x}\)