Introduction to...

$$\sec^2\theta =$$

If $$\displaystyle X=\tan 1^{0}+\tan 2^{0}+........+\tan 45^{0}$$ and $$\displaystyle y= -(\cot 46^{0}+\cot 47^{0}+.......+\cot 89^{0})$$ then find the value of $$(x + y)$$.

In a right angled triangle, $$\angle A = \theta$$ is an acute angle.

If $$\displaystyle \cos \Theta _{1}+\cos \Theta _{2}+\cos \Theta _{3}=3,$$ find $$\displaystyle \sin \Theta _{1}+\sin \Theta _{2}+\sin \Theta _{3}.$$

If in a rectangular, the angle between a diagonal and a side is 30$$^o$$ and the length of the diagonal is $$8$$ cm, then the area of the rectangle is _____ .

The value of  $$\displaystyle \sin ^{2}5^{\circ}+ \sin ^{2}10^{\circ}+\sin ^{2}15^{\circ}......+\sin ^{2}90^{\circ}$$ is equal to

If $$\displaystyle 3\cos ^{2}A=\cos 60^{\circ}+\sin ^{2}45^{\circ} $$ then find the value of $$\displaystyle \sec ^{2}A$$.

If $$\displaystyle25\sin ^{2}\theta +10\cos ^{2}\theta =15 $$ then find $$\displaystyle\cot  ^{2}\theta $$

In a right angled $$\triangle ABD$$, $$\angle B = 60^o$$ and $$\angle A = 30^o$$.

In a right angled $$\triangle ABD$$, $$\angle B = 60^o$$ and $$\angle A = 30^o$$, then $$\sin{60^o} =$$