If integral d x-s e c x-cosec x-tan x- x2-x-2-2 cos x-b-4-b-cos 2 x-c-d- then a-b-c is equal to

The correct option is D 4clearly, I= ∫sin^2 x cos^2 x/(sin x+cos x +1)^2dx =1/4∫ ( (sin x+cos x)^2 1 )^2/(sin x +cosx +1)dx =1/4∫ (sin x+cos x 1)^2 dx On simp ...

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Byju's Answer

Standard XII

Mathematics

Integrals of Mixed Powers of Sine and Cosine

If integral d...

Question

If integral $\frac{d x}{(s e c x + c o s e c x + t a n x + c o t x)^{2}} = \frac{x}{a} + \frac{\sqrt{2} c o s x + \frac{p}{4}}{b} + \frac{c o s 2 x}{c} + d,$ then a+b+c is equal to

-2

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-4

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none of these

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Solution

The correct option is B -4
clearly, $I = \int \frac{s i n^{2} x c o s^{2} x}{(s i n x + c o s x + 1)^{2}} d x = \frac{1}{4} \int \frac{{((s i n x + c o s x)^{2} - 1)}^{2}}{(s i n x + c o s x + 1)} d x = \frac{1}{4} \int (s i n x + c o s x - 1)^{2} d x$ On simplifying a + b + c = - 4

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If integral dx(secx+cosecx+tanx+cotx)2=xa+√2cosx+p4b+cos2xc+d, then a+b+c is equal to

The correct option is B -4clearly, I=∫sin2xcos2x(sinx+cosx+1)2dx=14∫((sinx+cosx)2−1)2(sinx+cosx+1)dx=14∫(sinx+cosx−1)2dx On simplifying a + b + c = - 4

If integral $\frac{d x}{(s e c x + c o s e c x + t a n x + c o t x)^{2}} = \frac{x}{a} + \frac{\sqrt{2} c o s x + \frac{p}{4}}{b} + \frac{c o s 2 x}{c} + d,$ then a+b+c is equal to

The correct option is B -4
clearly, $I = \int \frac{s i n^{2} x c o s^{2} x}{(s i n x + c o s x + 1)^{2}} d x = \frac{1}{4} \int \frac{{((s i n x + c o s x)^{2} - 1)}^{2}}{(s i n x + c o s x + 1)} d x = \frac{1}{4} \int (s i n x + c o s x - 1)^{2} d x$ On simplifying a + b + c = - 4