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

If tan40⁰ = λ, then \(\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } } \) =

\(\frac { sin(A-B) }{ cosAcosB } +\frac { sin(B-C) }{ cosBcosC } +\frac { sin(C-A) }{ cosCcosA } \) is

If tan x = \(\frac { -1 }{ \sqrt { 5 } } \) and x lies in the IV quadrant, then the value of cos x is ___________

Which of the following is incorrect?

Prove that \(sinx+sin2x+sin3x=sin2x(1+2cosx)\)

If a cos (x + y) = b cos (x - y), show that (a + b) tan x = (a - b) cot y.

Evaluate sin\(\left( \frac { -11\pi }{ 3 } \right) \).

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

Evaluate sin\(\left( cos^{ -1 }\left( \frac { 3 }{ 5 } \right) \right) \)

Prove that \({ tan }^{ -1 }\left( \frac { 1 }{ 7 } \right) +{ tan }^{ -1 }\left( \frac { 1 }{ 13 } \right) ={ tan }^{ -1 }\frac { 2 }{ 9 } \)

Show that \(\sin ^{ 2 }{ \frac { \pi }{ 18 } } +\sin ^{ 2 }{ \frac { \pi }{ 9 } } +\sin ^{ 2 }{ \frac { 7\pi }{ 18 } } +\sin ^{ 2 }{ \frac { 4\pi }{ 9 } } =2\)

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 sin (A + B)

Find the principal value of \(sin^{ -1 }\left( \frac { 1 }{ \sqrt { 2 } } \right) \).

Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x.

Simplify: \(\frac{cos(90°+\theta)sec(-\theta)tan(180°-\theta)}{sec(360°-\theta)sin(180°+\theta)cot(90°+\theta)}\)

Show that 4 sin A sin (60° +A).sin(60° - A) = sin 3A

If cot \(\theta\) (1 + sin \(\theta\)) = 4m and cot \(\theta\) (1 - sin \(\theta\)) = 4n, then prove that (m² - n²)² = mn

Two trees A and B are on the same side of a river. From a point C in the river the distance of trees A and B are 250 m and 300 m respectively. If the angle C is 45^o, find the distance between the trees.

Solve \(\sin { 2x } +\sin { 4x } +\sin { 6x } =0\)