Question

sin 75 - sin 15 / cos 15 - cos 75 = 1​

Answer 1

LHS

= COS(90- 75) - COS( 90- 15)° / COS 15° - COS 75°

= COS 15° - COS 75 ° / COS 15° - COS 75°

= 1

HENCE PROVED

Answer 2

sin ( 45 + 30 ) - tan 15 - cos ( 45 + 30 )

=> sin45.cos30 + cos45.sin30 - tan( 45 - 30 ) - (cos45 cos30 - sin45 sin30)

$= > \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} - \frac{1 - \frac{1}{ \sqrt{3} } }{1 +1 \times \frac{1}{ \sqrt{3} } } - \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ \\ = > \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } - \frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1} - \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ \\ = > \frac{1}{ \sqrt{2} } - \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \\ \\ = > \frac{1}{ \sqrt{2} } - \frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1 } \\ \\ = > \frac{1}{ \sqrt{2} } - \frac{3 - 2 \sqrt{3} + 1}{3 - 1} \\ \\ = > \frac{1}{ \sqrt{2} } - \frac{4 - 2 \sqrt{3} }{2} \\ \\ = > \frac{1}{ \sqrt{2} } - 2 + \sqrt{3}$

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