Question

Evaluate each of the following 2 sin² 30° − 3cos² 45° + tan² 60°

Answer 1

SOLUTION:

Given :  

2 sin² 30° - 3cos² 45° + tan² 60°          

= 2(1/2)² - 3(1/√2)² + (√3)²

[sin 30° = ½  , cos 45° =1/√2, tan 60° = √3]

= 2(1/4)  - 3(1/2) + 3

= (½ - 3/2) + 3

= (1 - 3)/2 + 3

= - 2/2 + 3

= -1 + 3 = 2

2 sin² 30° - 3cos² 45° + tan² 60° = 2

Hence , 2 sin² 30° - 3cos² 45° + tan² 60° = 2

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Answer 2

Answer :-


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To evaluate : 2 sin² 30° − 3cos² 45° + tan² 60°


Salutation :-

2 sin² 30° − 3cos² 45° + tan² 60°

= 2 × ( 1 / 2 )² - 3 × ( 1 / √2 )² + ( √3 )²

= 2 × 1 / 4 - 3 × 1 / 2 + 3

= 1 / 2 - 3 / 2 + 3

= ( 1 - 3 + 6 ) / 2

= 4 / 2

= 2


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Since ,

sin30° = 1 / 2

cos45° = 1 / √2

tan60° = √3

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