Question

Sec teta +tan teta is equal to 2/3 then sin teta is equals to?

Answer 1

Answer:

given :

sec ∅ + tan ∅ = 2/3

1/cos ∅ + sin ∅ / cos ∅ =  2/3            since sec ∅ = 1/ cos ∅    and

                                                                      tan ∅ = sin ∅ / cos ∅

(1 + sin ∅) / cos ∅ = 2/3

squaring on both sides

( 1+ sin ∅) (1 + sin ∅) / $cos^{2}$ ∅ = 4/9

( 1+ sin ∅) (1 + sin ∅) / ( 1 - $sin^{2}$∅) = 4/9         since  $cos^{2}$ x =  (1 - $sin^{2}$ x)

( 1+ sin ∅) (1 + sin ∅) / ( 1+ sin ∅) (1 - sin ∅) =4/9     since   $a^{2} - b^{2} = (a + b )( a - b)$

( 1+ sin ∅) / (1 - sin ∅) = 4/9

9 + 9 sin ∅ = 4 - 4 sin∅

13 sin ∅ = -5

sin ∅ = -5/13

Hope it helps !