Question

how to find question 20​

Answer 1

Theta is written as A.

Answer:

tanA. secA + sec^2 A = 1 / ( 1 - sinA )

Step-by-step explanation:

From the properties of trigonometric ratios :

• tanA = sinA / cosA ( A ≠ π / 2 )
• secA = 1 / cosA ( A ≠ π / 2 )
• 1 - sin^2A = cos^2 A

= > ( tanA. secA ) + sec^2A

= > { ( sinA / cosA ) x 1 / cosA } + 1 / cos^2 A

= > ( sinA / cos^2 A ) + 1 / cos^2 A

= > 1 / cos^2 A x ( sinA + 1 )

= > 1 / ( 1 - sin^2 A ) x ( sinA + 1 )

= > 1 / { ( 1 + sinA )( 1 - sinA ) } x ( sinA + 1 ) { 1 - sin^2 A = ( 1 + sinA )( 1 - sinA ), using a^2 - b^2 = ( a + b )( a - b ) }

= > 1 / ( 1 - sinA )

Hence, proved.