10. Find the exact value of cos(a – B) given the following. Simplify completely. Show formulas used and substitutions made. 3 37 sin (a)

Q: 9. Find the exact value of each expression. (i) 17T a. tan 6. b. cos 0- sec(0 - 2n) sin(-0) C. d.…

A: (a)

Q: evaluate / sin²(z) cos³(x) dx we use the identity sin²(x) + cos²(x) = 1 to obtain [ sin²(2)( cos(x)…

A: Given query is to find the substitution applied.

Q: Given Sin(A) = 3/5 with 0º < A < 90º and cos(B) = 4/5 with 270º < B < 360º, which expression gives…

A: Given- Given sinA = 35 with 0° &lt; A &lt; 90° and cosB = 45 with 270° &lt; B &lt; 360° To find-…

Q: 5. Verify that the expression is an identity: sin? 0 = sec 0- cos 0 cos 0 6. Verify that the…

A: 5. sin2θcos θ=sec θ-cos θ6. sec2x-11+tan2x=sin2x

Q: 3. Evaluate and solve for x. (No decimal values allowed) tan 30° sec60°sin90° esc-45 sec600 X(sin…

A: Put tan30°=1/√3, sin30°=1/2, sin90°=1 Cosec45°=√2, cos45°=1/√2 Then solve for x

Q: 3. Simplify the following expression completely: (sin x + cos x)² – 1

A:

Q: 3. Find the exact value. (a) sin 6 137 (b) сos 4 (c) tan 3 (d) csc 2

A: To Find the exact value:-  a) sin 7π6 = sin π+π6 = -sin π6 = - 32   b) cos 13π4 = cos 3π+π4 =…

Q: 10. Simplify (cos x- sin x)? - (sin x-cos x)'.

A:

Q: (2sin x) -1 Cos

A: cos(2 sin-1x) Let sin-1x=u Taking sin  function on both sides x=sin u

Q: Convert this identity to one using sine term(s) only. 1 - 2 cos2r = 2sin²r - 1 -1 - sin²r 1 -…

A: This question is based on conversion of Cos2r = 1 - Sin2r

Q: V2 + V6 66. Given that cos- 12 give the exact function values. 4 a. sin 12 b. sin- 12 с. sec 12

A: Given: cosπ12=2+64

Q: 1. Simplify the following: a. sin(180°-) cos(360°+0) cos(180 +0) tan(360°-0)

A:

Q: 9. sin ở In(cos 0) de

A: let I=∫sin θ ln(cosθ) dθ Integration By parts: ∫udu=uv-∫vdu u=ln( cosθ) ; du=1 cosθ-sinθdθ=-tanθdθ…

Q: a) Simplify the following expression. cos cos '(2x)+ si

A:

Q: cos x – 1.75 = -1 COS X sin(4x) = 2 – sin 4x 4 tan(2x) – 1 = 3

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.