Find the general solutions of\(\sqrt{3}\) sin x-cos x =2 ______.

The solution of the equation cos² \(\theta\) -+sin\(\theta\)+ 1=0lies in the interval ______.

If 4 sin²\(\theta=1\) then the values of \(\theta\) are ______.

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

If sin \(\theta\) + sin \(\phi\)= \(\alpha\) and cos\(\theta\) - cos\(\phi\)= b then tan\({\theta -\phi\over 2}\) is equal to ______.

In a\(\triangle\) ABC, if tan A +tanB+ tan C = o then cot A cot B cot C 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 tan \(\theta\) + sec \(\theta\) = e^x then cos\(\theta\) is equal to ______.

If tan\(\theta\) + cot \(\theta\) = 5 then tan³ \(\theta\) + cot³ \(\theta\) is equal to ______.

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

If x = r sin\(\alpha\) cos \(\beta\), y = r sin\(\alpha\) sin \(\beta\)and z = r cos\(\alpha\), then X² + y² + Z² is independent of ______.

In a ΔABC, if the sides are 7cm, 4\(\sqrt { 3 } \) cm and .\(\sqrt { 13 } \) cm, then the smallest angle is ______.

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

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