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RD Chapter 4 Inverse Trigonometric Functions Ex 4.11 Solutions

Question - 1 : -

Prove the following results:

(i) Tan-1 (1/7) + tan-1 (1/13) = tan-1 (2/9)

(ii) Sin-1 (12/13) + cos-1 (4/5) + tan-1 (63/16)= π

(iii) tan-1 (1/4) + tan-1 (2/9) = Sin-1 (1/√5)

Answer - 1 : -

(i) Given Tan-1 (1/7)+ tan-1 (1/13) = tan-1 (2/9)

Hence, proved.

(ii) Given Sin-1 (12/13)+ cos-1 (4/5) + tan-1 (63/16) = π

Consider LHS

Hence, proved.

(iii) Given tan-1 (1/4)+ tan-1 (2/9) = Sin-1 (1/ √5)

Question - 2 : - Find the value of tan-1 (x/y)– tan-1 {(x-y)/(x + y)}

Answer - 2 : -

Given tan-1 (x/y)– tan-1 {(x-y)/(x + y)}

Question - 3 : -

Answer - 3 : -


Question - 4 : -

Answer - 4 : -


Question - 5 : -

Answer - 5 : -


Question - 6 : -

Solve the followingequations for x :

Answer - 6 : -


Question - 7 : -

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Question - 8 : -

Answer - 8 : -


Question - 9 : -

Answer - 9 : -


Question - 10 : -

Solve the followingequations for x:

Answer - 10 : -


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