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

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

In a\(\triangle\) ABC, if tan A +tanB+ tan C = o then cot A cot B cot C is equal to______.

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

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

Find the degree measures corresponding to the following radian measures (use \(\pi\) = 22/7).\(({1\over6})^C\)

Find the degree measures corresponding to the following radian measures (use \(\pi\) = 22/7)-2^c

Find the values of tan 105^o

Find the general solutions of the following equations \(tan \ x={-1\over \sqrt{3}}\)

Prove that \({sin A+sin B\over cos A+cos B}\)=\(tan ({A+B\over 2})\)

Find the values of the trigonometric function \(sin(-750^o)\)

Find the general solutions of the following equations:
tan x + tan 2x + \(\sqrt{3}\) tan x tan 2x = \(\sqrt{3}\)

The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degrees, minutes and seconds.

Find the value of sin 75°.

Find the following values: sin 36°

If \(\underset { x\longrightarrow b }{ lim } \cfrac { { x }^{ 3 }-{ b }^{ 3 } }{ x-b } =\underset { x\longrightarrow 1 }{ lim } \cfrac { { x }^{ 4 }-1 }{ x1 } \)Find all possible value of b.

A tree stands vertically on a hill side which makes an angle of 15\(^{o}\)with the horizontal. From a point on the ground 35m down the hill from the base of the tree, the angle of elevation of the hop of tree is 60\(^{o}\). Find the height of the tree.

Find the general solution for each of the following equations:
sec² 2x = 1- tan 2x

prove that:
\({({sin \ 7x}+ sin 5x) +(sin 9x + sin 3x)\over (cos 7x + cos 5x) + (cos 9x + cos 3x)}=\tan6x\)