Home
Class 12
MATHS
Evaluate int (1)/(a sin x+ b cos x) dx w...

Evaluate `int (1)/(a sin x+ b cos x)` dx where `a, b in R and a^(2) +b^(2)ne 0 on R.`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(sqrt(a^(2) + b^(2))) " log " | tan ((x)/(2) + (alpha)/(2)) | ` + c
where cos `alpha = (a)/(r) , " sin "alpha = (b)/(r), r = sqrt(a^(2) + b^(2)) `
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - 1.6 (VERY SHORT ANSWER QUESTIONS)|18 Videos

  • INDEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - 1.6 (SHORT ANSWER QUESTIONS )|37 Videos

  • INDEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - 1.5( SHORT ANSWER QUESTIONS )|2 Videos

  • HYPERBOLA

    AAKASH SERIES|Exercise Exercise|6 Videos

  • LOGARITHMIC SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos

Similar Questions

Explore conceptually related problems

int (secx)/(a cos x+ b sin x)dx=

Evaluate int(1)/(cos^(2) x + sin 2x)dx

Evaluate int sin ^(2) x dx on R.

Evaluate int cos^3x sin x dx " on " R .

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that cos alpha cos beta = (c^(2) - b^(2))/(a^(2) + b^(2))

General solution of the equation a Cos x + b Sinx = c when a, b, c in R such that a^(2) + b^(2) ne 0 and a + c ne 0

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that sin alpha sin beta = (c^(2)-a^(2))/(a^(2) + b^(2))

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that sin alpha + sin beta = (2bc)/(a^(2) + b^(2))

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that cos alpha + cos beta = (2ac)/(a^(2) + b^(2))