Trig Identity

Geometry Level 2

What is the value of: sin³x cos³x tan³x sec³x csc³x cot³x ?

Note: Assume that 'x' is defined within a suitable domain, if any.

1 Undefined 0

Charley Shi by Charley Shi , 19, New Zealand

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.

2 solutions

Poca Poca
Jul 3, 2018

Using the definitions of the trigonometric functions, we get:

sin ⁡ 3 x ⋅ cos ⁡ 3 x ⋅ tan ⁡ 3 x ⋅ sec ⁡ 3 x ⋅ csc ⁡ 3 x cot ⁡ 3 x = sin ⁡ 3 x ⋅ cos ⁡ 3 x ⋅ sin ⁡ 3 x cos ⁡ 3 x ⋅ 1 cos ⁡ 3 x ⋅ 1 sin ⁡ 3 x ⋅ cos ⁡ 3 x sin ⁡ 3 x = 1 . \sin^3x \cdot \cos^3x \cdot \tan^3x \cdot \sec^3x \cdot \csc^3x \cot^3x =\sin^3x \cdot \cos^3x \cdot \frac{\sin^3 x}{\cos^3 x} \cdot \frac{1}{\cos^3 x} \cdot \frac{1}{\sin^3 x} \cdot \frac{\cos^3 x}{\sin^3 x}=\boxed{1}.

In fact, it's true for all possible exponents.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Edwin Gray
Jan 10, 2019

[ ( s i n ( x ) ∗ c s c ( x ) ] ∗ [ ( c o s ( x ) ∗ ( s e c ( x ) ] ∗ [ ( t a n ( x ) ∗ ( c o t ( x ) ] [(sin(x)*csc(x)]*[(cos(x)*(sec(x)]*[(tan(x)*(cot(x)] ^3 =(1 1 1)^3 = 1. Ed ray

0 Helpful 0 Interesting 0 Brilliant 0 Confused

1 pending report

Vote up reports you agree with

×

Problem Loading...

Note Loading...

Set Loading...