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Find the derivative of the following functions (it is to be un

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Find the derivative of the following functions (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{sin ( x + a )}{cos x}$

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Find the derivative of the following functions (it is to be understood that

a, b, c, d, p, q, r

and

s

are fixed non-zero constants and

m

and

n

are integers) :

\frac{sin ( x + a )}{cos x}

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Text solutionVerified

Let

f (x) = \frac{sin ( x + a )}{cos x}

Thus by quotient rule,

f^{'} (x) = \frac{cos x \frac{d}{d x} [ sin ( x + a ) ] - sin ( x + a ) \frac{d}{d x} cos x}{cos ^{2} x}

= \frac{cos x cos ( x + a ) - sin ( x + a ) ( - sin x )}{cos ^{2} x}

= \frac{cos x . cos ( x + a ) + sin x sin ( x + a )}{cos ^{2} x}

= \frac{cos ( x + a - x )}{cos ^{2} x} = \frac{cos a}{cos ^{2} x}

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Question Text	Find the derivative of the following functions (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers) : $\frac{sin ( x + a )}{cos x}$
Answer Type	Text solution:1
Upvotes	150