Question

please help solve this question.....
$\frac{cos \: 65}{sin25} - \frac{ \tan(20) }{ \cot(70) } - \sin(90) + \frac{ \cos(30 + \sin(60) ) }{1 + \cos(60 ) + \sin(30) }$
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Answer 1

Answer:

$\frac{\sqrt{3} -2}{2}$

Step-by-step explanation:

sin (90° - β) = cos β

tan (90° - β) = cot β

1). sin 25° = sin (90° - 65°) = cos 65° ⇒ cos 65° / sin 25° = 1

2). tan 20° = tan (90° - 70°) = cot 70° ⇒ tan 20° / cot 70° = 1

3). sin 90° = 1

4). [ sin 60° = sin (90° - 30°) = cos 30° = $\frac{\sqrt{3} }{2}$ ] ⇒

Numerator is ( $\frac{\sqrt{3} }{2}$ + $\frac{\sqrt{3} }{2}$ ) = √3

Denominator is (1 + $\frac{1}{2}$ + $\frac{1}{2}$ ) = 2

$\frac{\sqrt{3} }{2}$

Finally:

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

Answer 2

the answer is (√3-2) / 2