if sin a = cos a , find the value of 2 tan^2 a +sin^2a - 1
Answers
Answered by
17
sin a = cos a
sin a = sin( 90 - a )
a = 90 - a
a + a = 90°
2a = 90°
a = 45° ------: [ 1 ]
Now, we get that value of angle a is 45°
Therefore :-
2 tan² a + sin² a - 1
= > 2 tan² 45° + sin² 45° - 1
= > 2 ( 1 ) + ( 1 / √2 )² - 1
= > 2 + 1 / 2 - 1
= > 2 - 1 + 1 / 2
= > 1 + 1 / 2
= > ( 2 + 1 ) / 2
= > 3 / 2
sin a = sin( 90 - a )
a = 90 - a
a + a = 90°
2a = 90°
a = 45° ------: [ 1 ]
Now, we get that value of angle a is 45°
Therefore :-
2 tan² a + sin² a - 1
= > 2 tan² 45° + sin² 45° - 1
= > 2 ( 1 ) + ( 1 / √2 )² - 1
= > 2 + 1 / 2 - 1
= > 2 - 1 + 1 / 2
= > 1 + 1 / 2
= > ( 2 + 1 ) / 2
= > 3 / 2
Similar questions