Question

Sin square 300°+sin 240°.cos150° all over tan225°.sin270° Simplify without using a calculator

Answer 1

Answer:

Step-by-step explanation:

See the attachment.....

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Answer 2

Question:

$\frac{ {sin}^{2}300° + sin240°.cos150° }{tan225°.sin270°}$

Answer:

$\underline\bold{ \frac{- 3}{2}} \: is \: the \: value.$

Step-by-step explanation:

$\frac{ {sin}^{2}300° + sin240°.cos150° }{tan225°.sin270°}$

$= \frac{ {sin}^{2}(360° - 60°) + sin(180° + 60°).cos(180° - 30°) }{tan(180° + 45°). sin(180° + 90°)}$

$= \frac{ {sin}^{2}( - 60°) + sin60°. cos30° }{ tan45°. sin90° }$

$= \frac{ { (\frac{ \sqrt{3} }{2}) }^{2} - \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{3} }{2} }{1 \times 1}$

$= \frac{ \frac{ - 3}{4} - \frac{3}{4} }{ 1}$

$= \frac{ \frac{ - 6}{4} }{ 1}$

$\Rightarrow\boxed{ \frac{- 3}{2} }$

Identities used:

$\star sin60° = \frac{ \sqrt{3} }{2}$

$\star cos60° = \frac{ \sqrt{3} }{2}$

$\star tan45° = 1$

$\star sin90° = 1$