Question

HEYA...... RHYTHM HERE....
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. 20 points
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full explanation

Thanx

Answer 1

13.

Given sin47 + sin61 - sin11 - sin 25

= > (sin 47 - sin11) + (sin61 - sin25)

We know that sina - sinb = 2cos(a + b)/2 sin(a - b)/2

= > 2cos(47 + 11)/2 sin (47 - 11)/2 + 2cos(61 + 25)/2 sin(61 - 25)/2

= > 2 cos 29 sin 18 + 2 cos 43 sin 18

= > 2 sin 18(cos 29 + cos 43)

We know that cosA + cos B = 2cos(A + B)/2 cos(A-B)/2

= > 2sin 18(cos(29 + 43)/2) cos(43 - 29)/2

= > 2 sin18 cos 36 cos 7

$= \ \textgreater \ 2 cos 7 * \frac{ \sqrt{5} + 1 }{4} * \frac{ \sqrt{5} - 1 }{4}$

= > 2 * cos 7 * 2 * 1/4

= > 4 cos 7/(4)

= > cos 7.


(14).

$Given : \frac{cos^2 (33) - cos^2 (57)}{sin21 - cos 21}$

$= \ \textgreater \ \frac{sin^2(57) - sin^2(33)}{sin21 - sin69}$

We know that a^2 - b^2 = (a + b)(a - b)

$= \ \textgreater \ \frac{sin(57 + 33)sin(57 - 33)}{2cos \frac{21 + 69}{2}sin \frac{21 - 69}{2} }$

$= \ \textgreater \ \frac{sin90sin24}{-2cos 45sin24}$

$= \ \textgreater \ \frac{-sin90}{2cos45}$

$= \ \textgreater \ \frac{-1}{2 * \frac{1}{ \sqrt{2} } }$

$= \ \textgreater \ \frac{-1}{ \sqrt{2} }$


Hope this helps!