Find the value of cos3A - cos3A-cosA - sin3A - sin3A-sinA

Given expression requires the values of sin3A amp; cot3A sin3A = 3sinA 4sin^3A cos3A = 4cos^3A 3cosA Substituting the value of sin 3A and cos 3A Expr ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

Find the valu...

Question

Find the value of $\frac{c o s^{3} A - c o s 3 A}{c o s A}$ + $\frac{s i n^{3} A - s i n 3 A}{s i n A}$

__

Open in App

Solution

Given expression requires the values of sin3A & cot3A

sin3A = 3sinA - 4 $s i n^{3} A$

cos3A = 4 $c o s^{3} A$ - 3cosA

Substituting the value of sin 3A and cos 3A

Expression = $\frac{c o s^{3} A - (4 c o s^{3} A - 3 c o s A)}{c o s A}$ + $\frac{s i n^{3} A - 3 s i n A - 4 s i n^{3} A}{s i n A}$

$\frac{c o s^{3} A - 4 c o s^{3} A + 3 c o s A}{c o s A}$ + $\frac{- 3 s i n^{3} A + 3 s i n A}{s i n A}$

$\frac{- 3 c o s^{3} A + 3 c o s A}{c o s A}$ + $\frac{3 s i n A - 3 s i n^{3} A}{s i n A}$

-3 $c o s^{2} A$ + 3 + 3 -3 $s i n^{2} A$

6 - 3 $(s i n^{2} A + c o s^{2} A)$

6 - 3 = 3

Suggest Corrections

Similar questions

$\frac{s i n^{3} A + c o s^{3} A}{s i n A + c o s A} + \frac{s i n^{3} A - c o s^{3} A}{s i n A - c o s A} = 2$

Q. Prove that

\frac{S i n^{3} A + c o s^{3} A}{s i n A + c o s A} + \frac{S i n^{3} A - c o s^{3} A}{s i n A - c o s A} = 2

[4 MARKS]

Q. On simplifying

\frac{{sin}^{3} A + sin 3 A}{sin A} + \frac{{cos}^{3} A - cos 3 A}{cos A}

we get

$\frac{{cos}^{3} A - cos 3 A}{cos A}$ + $\frac{{sin}^{3} A - sin 3 A}{sin A} =$

Prove:

\frac{{c o s}^{3} A + {s i n}^{3} A}{c o s A + s i n A} + \frac{{c o s}^{3} A - {s i n}^{3} A}{c o s A - s i n A} = 2

Join BYJU'S Learning Program

Find the value of cos3A−cos3AcosA + sin3A−sin3AsinA __

Find the value of $\frac{c o s^{3} A - c o s 3 A}{c o s A}$ + $\frac{s i n^{3} A - s i n 3 A}{s i n A}$

__