Math, asked by tashi59, 6 hours ago

The value of 3 - sin2 60°/ tan 30° tan60° is​

Answers

Answered by CPSEKHAR
1

Step-by-step explanation:

Solution : Given that

3 - sin^2 60°/ tan 30° tan60°

= 3 - (√3 / 2)^2 / (1/√3 × √3 )

= 3-3/4

= (12-3)/4

= 9/4

3 - sin^2 60°/ tan 30° tan60° = 9/4

Answered by sangram0111
10

Given:

(Note: the correct question is- \[3 - \frac{{{{\sin }^2}60^\circ }}{{\tan 30^\circ \tan 60^\circ }}\])

To find: value of the expression.

Solution:

Know that, \[\sin 60^\circ  = \frac{{\sqrt 3 }}{2},\tan 30^\circ  = \frac{1}{{\sqrt 3 }}\] and \[\tan 60^\circ  = \sqrt 3 \]

Therefore,

\[ = 3 - \frac{{{{\left( {\frac{{\sqrt 3 }}{2}} \right)}^2}}}{{\frac{1}{{\sqrt 3 }} \times \sqrt 3 }}\]

\[ = 3 - \frac{{\frac{3}{4}}}{1}\]

\[ = 3 - \frac{3}{4}\]

\[ = \frac{{12 - 3}}{4}\]

\[ = \frac{9}{4}\]

Hence, the value of \[3 - \frac{{{{\sin }^2}60^\circ }}{{\tan 30^\circ \tan 60^\circ }}\] is \[  \frac{9}{4}\].

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