# CAT Practice : Trigonometry

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Max and Min value of the given expression

## Trigonometric Identities

Q.5: If cos A + cos2 A = 1 and a sin12 A + b sin10 A + c sin8 A + d sin6 A - 1 = 0. Find the value of $a + \frac{b}{c} + d$
1. 4
2. 3
3. 6
4. 1

Choice B. 3

## Detailed Solution

Given,
Cos A = 1- Cos2A
=) Cos A = Sin2 A
=) Cos2A = Sin4A
=) 1 – Sin2 A = Sin4 A
=) 1 = Sin4 A + Sin2 A
=) 13 = (Sin4A + Sin2A)3
=) 1 = Sin12 A + Sin6A + 3Sin8 A + 3Sin10 A
=) Sin12 A + Sin6A + 3Sin8 A + 3Sin10 A – 1 = 0
On comparing,
a = 1, b = 3 , c = 3 , d = 1
$a + \frac{b}{c} + d$ = 3
Always look out for Pythagorean triplets, we know that (8,15,17) is one
∴ 17 ($\frac{8}{17} cos⁡ A +\frac{15}{17}sinA)$

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