Question

(a) Find the exact value of each expression. (1) cot^{-1}(-?3) (2) cosleft(2sin^{-1}left(5/13 ight) ight) (3) csc^{-1}?2 (b) Simplify the expression (4) tan(sin^{-1} x) (5) sin(2arccos x) 6. (5 marks) - Prove the identity (1) cos(?/2 - x) = sin x (2) (sin x + cos x)^2 = 1 + sin 2x (3) tan^2 a - sin^2 a = tan^2 a sin^2 a (4) 2 csc 2t = sec t csc t

          (a) Find the exact value of each expression.
(1) cot^{-1}(-?3)     (2) cosleft(2sin^{-1}left(5/13
ight)
ight)     (3) csc^{-1}?2
(b) Simplify the expression
(4) tan(sin^{-1} x)     (5) sin(2arccos x)

6. (5 marks) - Prove the identity
(1) cos(?/2 - x) = sin x     (2) (sin x + cos x)^2 = 1 + sin 2x
(3) tan^2 a - sin^2 a = tan^2 a sin^2 a     (4) 2 csc 2t = sec t csc t

(a) Find the exact value of each expression.
(1) cot^-1(-?3) (2) cosleft(2sin^-1left(5/13
ight)
ight) (3) csc^-1?2
(b) Simplify the expression
(4) tan(sin^-1 x) (5) sin(2arccos x)

6. (5 marks) - Prove the identity
(1) cos(?/2 - x) = sin x (2) (sin x + cos x)^2 = 1 + sin 2x
(3) tan^2 a - sin^2 a = tan^2 a sin^2 a (4) 2 csc 2t = sec t csc t

Added by Eric W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/30/2023

Step 1

Therefore, $\cot^{-1}(-\sqrt{3}) = \boxed{-\frac{\pi}{3}}$. (2) $\cos(2\sin^{-1}(13))$ Let $y = \sin^{-1}(13)$. Then, $\sin(y) = 13$. We can use the double angle formula for cosine: $\cos(2y) = 1 - 2\sin^2(y) = 1 - 2(13^2) = \boxed{-337}$. (3) Show more…

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Find the exact value of each expression: (a) (1) cot^{-1}(-√3) (2) cosleft(2sin^{-1}left(5/13 ight) ight) (3) csc^{-1}√2 (b) Simplify the expression (4) tan(sin^{-1} x) (5) sin(2arccos x) 6. (5 marks) - Prove the identity (1) cos(π/2 - x) = sin x (2) (sin x + cos x)^2 = 1 + sin 2x (3) tan^2 a - sin^2 a = tan^2 a sin^2 a (4) 2 csc 2t = sec t csc t