Question

Evaluate each of the following $\frac{sin30^{0}-sin90^{0} +2cos0^{0} }{tan30^{0 }tan60^{0} }$

Answer 1

SOLUTION :  

Given :

sin 30°  - sin 90° + 2 cos 0°/ tan 30° tan 60°

= (½ - 1 + 2× 1) / (1/√3 ×√3)

[sin 30°=½,  - sin 90° = 1, cos 0° = 1,  tan 30° = 1/√3 , tan 60°= √3]

= (½ - 1 + 2) / (√3/√3)

= (½ +1) / 1

= ((1×1 + 1×2) / 2)  

[By taking L.C.M of 2 & 1. L.C.M is 2]

= (1 + 2)/2

= 3/2  

sin 30°  - sin 90° + 2 cos 0°/ tan 30° tan 60° = 3/2  

Hence, sin 30°  - sin 90° + 2 cos 0°/ tan 30° tan 60° = 3/2  

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer :-

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( sin 30°  - sin 90° + 2 cos 0° ) / ( tan 30° tan 60° )

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

=> ( 1 / 2 - 1 + 2 ) / 1

=> 1 / 2 + 1

=> ( 2 + 1 )/ 2

=> 3 / 2

•°• The required Answer is 3 / 2

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Since ,

sin 30°=½

sin 90° = 1

cos 0° = 1

tan 30° = 1/√3

tan 60°= √3

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