Question

If A and Bare supplementary angles, then `sin^2  "A"/2 + sin^2  "B"/2` = ______.

Options

• `1/3`

• 1

• `1/2`

• 0

Answer 1

If A and B are supplementary angles, then `sin^2  "A"/2 + sin^2  "B"/2` = 1.

Explanation:

Given, A and Bare supplementary angle

∴ A + B = 180°

`("A + B")/2 = 90°`

`"B"/2 = 90^circ - "A"/2`

∴ `sin^2  "A"/2 + sin^2  "B"/2`

`= sin^2  "A"/2 + sin^2 (90^circ - "A"/2)`

`= sin^2  "A"/2 + cos^2  "A"/2`

= 1