Q12 of 45 Page 1

Show that:

OR


Solve the following equation:


To prove:


Let, y =


∴ we can say that, we have to prove: tan y =


⇒ 2y =


⇒ sin 2y = 3/4


As we know that: sin 2y =


∴


∴ 8 tan y = 3 + 3 tan2y


⇒ 3 tan2y – 8tan y + 3 = 0


⇒ tan y =


⇒ tan y =


∴ tan y = or tan y =


Hence, tan y =


OR


Given:


We have to solve for x.


Let, y =


⇒ x = tan y


∴ LHS = cos y =


As, RHS =


Let, cot-1(3/4) = θ


∴ cot θ = 3/4


⇒ sin θ =


⇒ RHS = sin θ = 4/5


As, LHS = RHS {given}


⇒


⇒ 5 = 4√(1+x2)


Squaring both sides, we have-


⇒ 25 = 16(1+x2)


⇒ 25 = 16 + 16x2


⇒ 9 = 16x2


⇒ x2 = 9/16


∴ x = ±√(9/16) = ±3/4


More from this chapter

All 45 →
10

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue). If the total revenue (in rupees) received from the sale of x units of a product is given by R(x) =3x2 +36x + 5, find the marginal revenue when x = 5, and write which value does the question indicate.

 11

Consider f : R+→ [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f–1 of given by where R+ is the set of all non-negative real numbers.

 13

Using properties of determinants, prove the following:

 14

If yx = ey – x, prove that