Evaluate 2 cosec square thirty degree plus sin square sixty degree minus 3/4 tan square thirty degree
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Solution :
2cosec² 30° + sin² 60° - ( 3/4 )tan²30°
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we know that ,
i ) cosec 30° = 2
ii ) sin60° = √3/2
iii ) tan 30° = 1/√3
******************"****************†**
= 2 × ( 2 )² + ( √3/2 )² - ( 3/4 ) ( 1/√3 )²
= 2 × 4 + 3/4 - ( 3/4 ) × ( 1/3 )
= 8 + 3/4 - 1/4
= 8 + ( 3/4 - 1/4 )
= 8 + 2/4
= 8 + 1/2
= 17/2
••••
2cosec² 30° + sin² 60° - ( 3/4 )tan²30°
***********************************
we know that ,
i ) cosec 30° = 2
ii ) sin60° = √3/2
iii ) tan 30° = 1/√3
******************"****************†**
= 2 × ( 2 )² + ( √3/2 )² - ( 3/4 ) ( 1/√3 )²
= 2 × 4 + 3/4 - ( 3/4 ) × ( 1/3 )
= 8 + 3/4 - 1/4
= 8 + ( 3/4 - 1/4 )
= 8 + 2/4
= 8 + 1/2
= 17/2
••••
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