Question

Question 13: Find the value of tan 1/2 [sin¯¹ 2x/1+x + cos¯¹ 1-y²/1+y²] , |x| <1, y>0 and xy <1

Class 12 - Math - Inverse Trigonometric Functions

Answer 1

Refer to the attachment :-
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formulas used ---
•sin-¹ (2x/1+x²) = 2tan-¹x
•cos-¹ (1- y²/1+y²) = 2tan-¹ y

•tan-¹x + tan-¹y = tan-¹ (x+y/1-xy)

Answer 2

Hey there!!!

tan 1/2 [ sin¯¹ 2x/1+x + cos¯¹ 1-y²/1+y²] |x| <1, y>0 and xy <1

Now, from the attachment,

=> tan 1/2 [ sin¯¹ 2x/1+x + cos¯¹ 1-y²/1+y²]
=> tan 1/2 [2tan¯¹ x +2tan¯¹ y]
=> tan [ tan¯¹ x +tan¯¹ y]
=> tan [tan¯¹ (x+y / 1-xy)]
=> x+y / 1-xy

Hope it helps....