\(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

Let f_k(x) = \(\frac { 1 }{ k } \)[sin^kx + cos^kx] where x\(\in \)R and k ≥ 1. Then f₄(x) - f₆(x) =

If sin α + cos α = b, then sin 2α is equal to

If cosec x + cot x = \(\frac { 11 }{ 2 } \) then tan x = ___________

The value of sin²\(\frac { 5\pi }{ 12 } -sin^{ 2 }\frac { \pi }{ 12 } \) is ___________

sin² \((22{1\over 2}^o)\) is ____________ 

In \(\triangle\)ABC, \(\hat{C}\) = 90° then a cos A + b cos B is _______________

The value of tan 1° tan 2° tan 3°...tan 89° is ____________ 

If cos θ + \(\sqrt{3}\) sin θ = 2 and θ∈[0, 2π] then θ is _______________

The numerical value of tan^-11 + tan^-12 + tan^-13 = _______________

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

Prove that sin (A + B) sin (A - B) = sin² A - sin² B.

If A + B + C =\(\frac { \pi }{ 2 } \), prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C

Prove that \(\frac { cos(2\pi +x)cosec(2\pi +x)tan\left( \frac { \pi }{ 2 } +x \right) }{ sec\left( \frac { \pi }{ 2 } +x \right) cos.cot(\pi +x) } \)= 1

Find the general solution of \(\sqrt { 3 } \) sec 2x = 2

Find the value of sin 34° + cos 64° - cos 4°.

Find the principal value of sin^-1\(({\sqrt{3}\over2})\)

Find the values of cot(660°).

Express each of the following angles in radian measure
30⁰

Find the degree measure corresponding to the following radian measure; \(\frac { \pi }{ 3 } \)

A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie ( s sector of the circle with thickness) of radius 16 cm and thickness 4 mm. Find the angle of the sector

Show that \(\cot { \left( 7\frac { 1° }{ 2 } \right) } =\sqrt { 2 } +\sqrt { 3 } +\sqrt { 4 } +\sqrt { 6 } \)

In a \(\triangle\)ABC, prove that (b + c) cos A +(c + a) cos B + (a + b) cos C = a + b + c