Top

Trigonometric Identities Calculator
Top
An identity is something which holds good for any variable. Trigonometric identity are the identities used for the trigonometric functions.
Trigonometric Identities Calculator calculates the values of trigonometric functions if the variables U and V are given.

## Steps for Trigonometric Identities Solver

Step 1 :

Read the problem. Given are the variables of U and V.

Step 2 :

Substitute the given values in the identities, we get

sin U + sin V = 2 sin $\frac{U + V}{2}$ cos $\frac{U - V}{2}$
sin U - sin V = 2 cos $\frac{U + V}{2}$ sin $\frac{U - V}{2}$
cos U + cos V = 2 cos $\frac{U + V}{2}$ cos $\frac{U - V}{2}$
cos U - cos V = - 2 sin $\frac{U + V}{2}$ sin $\frac{U - V}{2}$

If we are interested to find the angle of product form then use product to sum form:

sin U sin V = $\frac{1}{2}$[cos(u - v) - cos(u + v)]

cos U cos V = $\frac{1}{2}$[cos(u - v) + cos(u + v)]

sin U cos V = $\frac{1}{2}$[sin(u + v) + sin(u - v)]

cos U sin V = $\frac{1}{2}$[sin(u + v) - sin(u - v)]

## Problems on Trigonometric Identities Solver

1. ### Calculate the value of trigonometric function.sin 750. sin 150

Step 1 :

Given: U = 750

V = 150

Step 2 :

Using the identity formula

sin U sin V = $\frac{1}{2}$[cos(u - v) - cos(u + v)]

sin750.sin150 = $\frac{1}{2}$ [cos(750 - 150) - cos(750 + 150)]

= $\frac{1}{2}$ [cos 600 - cos 900 ]

= $\frac{1}{2}$ [$\frac{1}{2}$ - 0]

sin750.sin150 = 0.25.

2. ### Find the value of the following:sin 750 - sin 150

Step 1 :

given: U = 750

V = 150

Step 2 :

Using the identity formula:

sin U - sin V = 2 cos $\frac{U + V}{2}$ sin $\frac{U - V}{2}$

sin 750 - sin 150 = 2 cos $\frac{75^{0} + 15^{0}}{2}$ sin $\frac{75^{0} - 15^{0}}{2}$

= 2 $\times$ $\frac{1}{\sqrt{2}}$ $\times$ $\frac{\sqrt{3}}{2}$

= 0.707