Subscribe to our ▶️YouTube channel🔴 for the latest videos, updates, and tips.
Home | About Us | Contact Us | Privacy | Math Blog
We will learn how to prove the property of the inverse trigonometric function arcsin(x) + arccos(x) = π2.
Proof: Let, sin−1 x = θ
Therefore, x = sin θ
x = cos (π2 - θ), [Since, cos (π2 - θ) = sin θ]
⇒ cos−1 x = π2 - θ
⇒ cos−1 x= π2 - sin−1 x, [Since, θ = sin−1 x]
⇒ sin−1 x + cos−1 x = π2
Therefore, sin−1 x + cos−1 x = π2. Proved.
Solved examples on property of inverse circular
function sin−1
x + cos−1 x
=
π2.
1. Prove that sin−1 45 + sin−1 513 + sin−1 1665 = π2
Solution:
sin−1 45 + sin−1 513 + sin−1 1665
= (sin−1 45 + sin−1 513) + sin−1 1665
= sin−1(45√1−(513)2)+513√1−(45)2) + sin−1 1665
= sin−1 (45 × 1213 + 513 × 35) + sin−1 1665
= sin−1 6365 + sin−1 1665
= cos−1√1−(6365)2) + sin−1 1665
= cos−1 1665 + sin−1 1665
= π/2, since sin−1x+cos−1x=π2
Therefore, sin−1 45 + sin−1 513 + sin−1 1665 = π2. Proved.
2. Solve the trigonometric equation: sin−1 5x + sin−1 12x = π2
Solution:
sin−1 5x + sin−1 12x = π2
⇒ sin−1 12x = π2 - sin−1 5x
⇒ sin−1 12x = cos−1 5x, [Since, we know that, sin−1 5x + cos−1 5x = π2]
⇒ sin−1 12x = sin−1 √x2−25x
⇒ 12x = √x2−25x
⇒ √x2−25 = 12, [Since, x ≠ 0]
⇒ x2 - 25 = 144
⇒ x2 = 144 + 25
⇒ x2 = 169
⇒ x = ± 13
The solution x = - 13 does not satisfy the given equation.
Therefore the required solution is x = 13.
● Inverse Trigonometric Functions
11 and 12 Grade Math
From arcsin x + arccos x = π/2 to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Jul 18, 25 10:38 AM
Jul 17, 25 01:06 AM
Jul 17, 25 12:40 AM
Jul 16, 25 11:46 PM
Jul 16, 25 02:33 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.