1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
8104911739

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

022-62211530

Mon to Sat - 11 AM to 8 PM

# Prove - sin5x-2sin3x+sinx /cos5x-cosx = tanx

Asked by prashant.jain 24th May 2010, 12:43 PM

We have explained the steps, please also refer to the solution in book, and apply the steps we listed below.

(sin5x-2sin3x+sinx) /(cos5x-cosx) =

In the numerator we can write for sin5x + sinx = 2 sin3x cos2x, using the result,

sinA + sinB = 2sin((A+B)/2)cos((A-B)/2), and here A = 5x and B = x.

Similarly for the denominator we can write,  cos5x - cosx = -2 sin3x sin2x,

cosA - cos B = -2sin((A+B)/2)sin((A-B)/2), and here A = 5x and B = x.

After this step, the next step is to take out sin3x common in numerator and denominator which cancels out leaving,

(1-cos2x)/sin2x,

Now make the final substitution using the trignometric results,

sin2A = 2sinAcosA and cos2A = cos2A - sin2A = 1 - 2sin2A.

After this substitution rest step is just algebraic manipulations to get the final result.

Regards,

Team,

TopperLearning.

Answered by Expert 24th May 2010, 6:34 PM
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

You have rated this answer 10/10