If cos 28⁰+ sin 28⁰ = k³, then cos 17⁰ is equal to

If \(\pi <2\theta <\frac { 3\pi }{ 2 } \), then \(\sqrt { 2+\sqrt { 2+2cos4\theta } } \) equals to

If cos pፀ + cos qፀ = 0 and if p ≠ q, then ፀ is equal to (n is any integer)

In a triangle ABC, sin²A + sin²B + sin²C = 2, then the triangle is

The triangle of maximum area with constant perimeter 12m

A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 30⁰. If after 100 km, the target has an angle of depression of 60⁰, how far is the target from the fighter jet at that instant?

Suppose that a satellite in space, an earth station and the centre of earth all in the same plane. Let r be the radius of earth and R be the distance from the centre of earth to the satellite. Let d be the distance from the earth station to the satellite. Let 30 be the angle of elevation from the earth station to the satellite. If the line segment connecting earth station and satellite substends angle α at the centre of earth, then prove that d =\(\sqrt { 1+\left( \frac { r }{ R } \right) ^{ 2 }-2\frac { r }{ R } cos\alpha } \) .

If x = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n } } \theta ;\) y = \(y=\sum _{ n=0 }^{ \infty }{ { sin }^{ 2n } } \theta \)  and z = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n }\theta } \) sin²ⁿ\(\theta \), 0 < \(\theta \) < \(\frac { \pi }{ 2 } \), then show that xyz = x+y+z  
Hint :1+x+x²+x³+.......= \(\frac { 1 }{ 1-x } \), where \(\left| x\right| \)< 1].

If sin A = \(\frac{3}{5}\) and cos B = \(\frac{9}{41}\), 0 < A < \(\frac{\pi}{2}\), 0 < B < \(\frac{\pi}{2}\). Find the value of cos (A - B)

If \(\cos { \left( \alpha -\beta \right) } +\cos { \left( \beta -\gamma \right) } +\cos { \left( \gamma -\alpha \right) } =\frac { -3 }{ 2 } \) then prove that \(\cos { \alpha } +\cos { \beta } +\cos { \gamma } =\sin { \alpha } +\sin { \beta } +\sin { \gamma } =0\)

Prove that (1 + sec 2\(\theta\)) (1 + sec 4\(\theta\)) ... (1 + sec 2ⁿ\(\theta\)) = tan 2ⁿ\(\theta\) cot \(\theta\).

If \(\frac { cos^{ 4 }\alpha }{ { cos }^{ 2 }\beta } +\frac { { sin }^{ 4 }\alpha }{ { sin }^{ 2 }\beta } =1\) prove that \({ sin }^{ 4 }\alpha +{ sin }^{ 4 }\beta =2{ sin }^{ 2 }\alpha { sin }^{ 2 }\beta\)

Find a quadratic equation whose roots are sin 15^o and cos 15^o