If cos 9α = sinα and 9α < 90° , then the value of tan5α is
a. 1/√3
b. √3
c. 1
d. 0
Solution:
Given, cos 9α = sin α
Given, 9α < 90°
We have to find the value of tan5α.
Since 9α < 90°, 9α is an acute angle.
Using the trigonometric ratios of complementary angles,
sin (90° - A) = cos A
So, cos 9α = sin(90° - 9α)
Now, sin(90° - 9α) = sin α
90° - 9α = α
On simplification,
α + 9α = 90°
10α = 90°
α = 90°/10
α = 9°
To find tan5α
Substitute the value of α,
tan 5α = tan(5 × 9)
= tan 45°
Using the trigonometric ratio of angles,
tan 45° = 1
✦ Try This: If sin 5α = cosα and 5α < 90° , then the value of cos3α is
Given, sin 5α = cosα
Given, 5α < 90°
We have to find the value of cos3α
Using the trigonometric ratios of complementary angles,
cos (90° - A) = sin A
So, sin 5α = cos (90°- 5α)
Now, cos (90°- 5α) = cos α
90° - 5α = α
90° = 5α + α
90° = 6α
α = 90°/6
α = 15°
To find cos 5α
cos 5α = cos 5(15)
= cos 45°
Using the trigonometric ratio of angles,
cos 45° = 1/√2
Therefore, the value of tan5α is 1/√2
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 7
If cos 9α = sinα and 9α < 90° , then the value of tan5α is a. 1/√3, b. √3, c. 1, d. 0
Summary:
If cos 9α = sinα and 9α < 90° , then the value of tan5α is 1
☛ Related Questions:
visual curriculum