The pdf contains multiple type questions on the topic INVERSE TRIGONOMETRY.
The pdf contains the most important questions and covers all the topics in depth.
Answers have been also given on the last page.
Sl. Question:
No
1. 5𝜋 2𝜋
If 𝑥 = tan−1 ( 𝑡𝑎𝑛 ) and 𝑦 = tan−1 (−𝑡𝑎𝑛 ) , then
4 3
A) 4𝑥 = 3𝑦
B) 3𝑥 = 4𝑦
C) 𝑥 − 𝑦 = 𝜋/8
D) 𝑥 − 𝑦 = 𝜋/6
2. 4 2
The value of tan( cos −1 5 + tan−1 3) is :
13
A) 6
17
B) 6
19
C) 6
23
D) 6
3. 2𝜋
If sin−1 𝑥 + sin−1 𝑦 = , then the value of cos −1 𝑥 + cos −1 𝑦 is :
3
𝜋
A) 3
𝜋
B) 6
2𝜋
C) 3
5𝜋
D) 3
𝜋
4. If sin−1 𝑥 − cos −1 𝑥 = , then 𝑥 is equal to:
6
1
A) 2
1
B) − 2
√3
C) 2
√3
D) − 2
5. 2𝜋 𝜋
The value of cos −1 ( 𝑐𝑜𝑠 ) + sin−1 (𝑠𝑖𝑛 )is :
3 3
ZIET, BHUBANESWAR Page 1
, 𝜋
A) 2
4𝜋
B) 3
C) 𝜋
D) 3𝜋/4
6. 3
The value of cos[tan−1 4] is :
3
A) 5
3
B) 4
4
C) 5
4
D) 3
7. 1
If 𝑥 = cot −1 ( − 5) and 𝑥 lies in 2nd quadrant , then the value of 𝑠𝑖𝑛𝑥 is :
1
A)
√26
1
B) −
√26
5
C)
√26
5
D) −
√26
8. 1
If 𝑥 = sin−1 ( − 2) + 2cos −1 (−
√3
) , then 𝑥 is
2
𝜋
A) 2
𝜋
B) − 2
3𝜋
C) 2
5𝜋
D) 6
9. The value of sin[cot −1 { cos(tan−1 1)}] is :
3
A) √2
2
B)√3
√3
C) 2
1
D) √2
10. The value of 𝑠𝑒𝑐 2 [tan−1 2] + 𝑐𝑜𝑠𝑒𝑐 2 [cot −1 3] is :
ZIET, BHUBANESWAR Page 2
, A) 5
B) 10
C)15
D) 20
11. If 4 sin−1 𝑥 + cos −1 𝑥 = 𝜋 , then the value of x is :
1
A) 2
1
B)
√2
√3
C)
2
D) 1
12. The value of sin−1 (𝜋 √𝑥) + cos −1 (𝜋√𝑥) is :
A) 𝜋
𝜋
B) 2 √𝑥
C) 𝜋√𝑥
𝜋
D) 2
13. 2𝜋
If tan−1 𝑥 +2 cot −1 𝑥 = , then the value of x is
3
A) 3
B) √3
√3−1
C)
√3+1
1
D)
√3
14. Which of the following corresponds to the principal value branch of cot −1 𝑥
A) [0, 𝜋 ]
B) (0, 𝜋 )
𝜋 𝜋
C) [ − 2 , 2 ]
𝜋 𝜋
D) ( − 2 , 2 )
𝜋 𝜋
15. If tan−1 𝑥 = 10 for some real values of x , then the value of cot −1 𝑥 is :A) 5
2𝜋
B) 5
3𝜋
C)
5
ZIET, BHUBANESWAR Page 3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller bansal25srishti. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
