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

If tan \(\theta\) + sec \(\theta\) = e^x then cos\(\theta\) is equal to ______.

In a \(\triangle \)ABC, if a=3, b=4 and c=5, then find angle C.

In any triangle, if angle are in the ratio 1:2:3, then find their corresponding sides.

Find the radian measures corresponding to the following degree measures: 10° 18' 30".

The difference between two acute angles of a right angled triangle is \(2\pi\over 5\)radians. Find the angles in radians

Find the values of other five trigonometric functions sin\(\theta\) =\({3\over5}\) ,\(\theta\) lies in third quadrant

Convert the following into radians.
-47^o 30'

Find the value of \(sin^{ 2 }\frac { \pi }{ 6 } +cos^{ 2 }\frac { \pi }{ 6 } +sin^{ 2 }\frac { \pi }{ 4 } \)

If cosec \(A=\frac { x }{ y } \), then find the value of cot A.

Find the values of the trigonometric function sec\(({25\pi\over3})\)

Find the general solutions of the following equations:
tan x + tan\(({x+{\pi\over3}})+tan({x+{2\pi\over3}})=3\)

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.

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)

Find the value of \([1+cos{\pi\over 8}][1+cos{3\pi\over 8}][1+cos{5\pi\over 8}][1+cos{{7\pi\over8}}]\)

Find sin\({x\over2},cos{x\over2} and \ tan {x\over2}\) in each of the following: sin x =\({1\over4}\),x in quadrant II.