Trigonometry! #135

Geometry Level 2

If A A is an obtuse angle, then find the value of the following expression. sin ⁡ 3 A − cos ⁡ 3 A sin ⁡ A − cos ⁡ A + sin ⁡ A 1 + tan ⁡ 2 A − 2 tan ⁡ A cot ⁡ A \frac{\sin^{3}A-\cos^{3}A}{\sin A - \cos A} + \frac{\sin A}{\sqrt{1+\tan^{2}A}} - 2\tan A \cot A

This problem is part of the set Trigonometry .


The answer is -1.

Omkar Kulkarni by Omkar Kulkarni , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Omkar Kulkarni
Feb 20, 2015

sin ⁡ 3 A − cos ⁡ 3 A sin ⁡ A − cos ⁡ A + sin ⁡ A 1 + tan ⁡ 2 A − 2 tan ⁡ A cot ⁡ A \frac{\sin^{3}A-\cos^{3}A}{\sin A - \cos A}+\frac{\sin A}{\sqrt{1+\tan^{2}A}}-2\tan A\cot A

= ( sin ⁡ A − cos ⁡ A ) ( sin ⁡ 2 A + sin ⁡ A cos ⁡ A + cos ⁡ 2 A ) sin ⁡ A − cos ⁡ A + sin ⁡ A sec ⁡ 2 A − 2 = \frac{(\sin A - \cos A)(\sin^{2}A+\sin A\cos A + \cos^{2} A)}{\sin A - \cos A}+\frac{\sin A}{\sqrt{\sec^{2} A}}-2

= 1 + sin ⁡ A cos ⁡ A − 2 + sin ⁡ A ± sec ⁡ A = 1+\sin A \cos A - 2 + \frac{\sin A}{\pm\sec A}

As A A is an obtuse angle, sec ⁡ A \sec A will be negative. Hence the expression becomes

− 1 + sin ⁡ A cos ⁡ A − sin ⁡ A cos ⁡ A -1 + \sin A \cos A - \sin A \cos A

= − 1 = \boxed{-1}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...