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

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

\(\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx } \) is equal to

cos 35⁰ + cos 85⁰ + cos 155⁰ = _______________

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

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

If 2 sin θ + 1 = 0 and \(\sqrt{3}\) tan θ = 1, then the most general value of θ is _______________

Area of triangle ABC is _______________

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.

The product of first n odd natural numbers equals

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?

Two vehicles leave the same place P at the same time moving along two different roads. One vehicle moves at an average speed of 60 km/hr and the other vehicle moves at an average speed of 80 km/hr. After half an hour the vehicle reach the destinations A and B. If AB subtends 60^o at the initial point P, then find AB.

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 tan² \(\theta\) = 1 - k², Show that sec \(\theta\) + tan³ \(\theta\) cosec \(\theta\) = (2 -k²)^3/2. Also, find the value of k for which this result holds

Prove that cos (A + B) cos C - cos (B + c) cos A = sin B sin (C - A)

If tan x = \(\frac{n}{n+1}\) and tan y = \(\frac{1}{2n+1}\), find tan (x + y).

Find the values of sin (-45°).

Express each of the following product as a sum or difference. cos 110° sin 55°.

Express each of the following angles in radian measure
135⁰

Find the degree measure corresponding to the following radian measure; \(\frac { 2\pi }{ 5 } \)

Find the values of cos 2A, A lies in the first quadrant, when cos A = \(\frac{15}{17}\)

Prove that \(\tan { \left( \frac { \pi }{ 4 } +\theta \right) } -\tan { \left( \frac { \pi }{ 4 } -\theta \right) } =2\tan { 2\theta } \)

Find the value of \(sin\left( 22\frac { 1^{ 0 } }{ 2 } \right) \)

Prove that \(\frac { sin4x+sin2x }{ cos4x+cos2x } =tan3x\)

Prove that \(\frac { sin(4A-2B)+sin(4B-2A) }{ cos(4A-2B)+cos(4B-2A) } =tan(A+B)\)

In \(\triangle\)ABC, Prove the following
\(\frac { asin(B-C) }{ { b }^{ 2 }-{ c }^{ 2 } } =\frac { bsin(C-A) }{ { c }^{ 2 }-{ a }^{ 2 } } =\frac { csin(A-B) }{ { a }^{ 2 }-{ b }^{ 2 } } \)

Express each of the following as a product.
cos 65^o + cos 15^o

Suppose two radar stations located 100 km apart, each detect a fighter aircraft between them. The angle of elevation measured by the first station is 30°, whereas the angle of elevation measured by the second station is 45°. Find the altitude of the aircraft at that instant.