Question Bank - Mathematics

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Let sin 2? = cos 3?, where ? is acute angle. What is the value of 1 + 4 sin ?? (given that \(\sin 18^\circ =\frac{\sqrt 5 - 1}{4}\))

A.
\(\sqrt 3\)
B.
2
C.
\(\sqrt 5\)
D.
3

Solution:

Concept:If A + B = 90° thensin A = cos BCalculation:Given that, sin 2? = cos 3?We know that sin A = cos B then A + B = 90° ? 2? + 3? = 90° ? 5? = 90° ? ? = 18° Hence, required value 1 + 4 sin ? ? 1 + 4 sin 18° ? 1 + 4((?5 - 1)/4) [? \(\sin 18^\circ =\frac{? 5 - 1}{4}\)]? 1 + ?5 - 1 = ?5? 1 + 4 sin ? = ?5

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