Use induction onn to prove that, for all integers n > 1, we have cos(nº) sin(n0) - sin(n®) cos(n®). A"

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Q: that "C₁ sin 2x + "C₂ sin 4x + "C3 sin 6x 1+ "C₁ cos2x+ "C₂ cos 4x + "C3 cos E x; where ne N

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Q: dx. sin(2x? + 1) Evaluate In|csc(2a? + 1) –- cot(2a² + 1)| + C 4 O - cos(2x? +1) + C O 4 ln|csc(2a?…

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Q: Which of the following is equal to cos A cos B? 1 [A] [sin(4 + B) – sin(A – B)] 1 [B] [sin(A + B) +…

A: Use trigonometric identities.

Q: •*/3 2 sin z dæ Compute O -1 O -2 O 2 O 1

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Q: Prove that |cos(a) - cos(b)| ≤ |a - b| (for all real numbers a and b), through the Mean Value…

A: To prove: cosa-cosb≤a-b

Q: Is the following indentity true? 1-sec(r) _ cos(r)-1 1+sec(x) cos(x)+1

A: We have to identify that the identity 1-secx1+secx=cosx-1cosx+1 is true or not. We know that…

Q: Cos I 12. secx + tan x 1. sin x

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Q: kn sin 11) Evaluate k = 0

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Q: If tan then 1– 2 1+ z2 COS X 8 |N

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Q: Use mathematical induction to prove that, for any positive integer n, we have: cOS Tn = (-1)", sin…

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Q: Prove that "C, . (n-r) COS r=0 2ræ n = -n.2n-1.cos n T - n

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Q: Find the values of x in 4 cos2 x = 1

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Q: 10. Prove that 7/2 sin 0 cos (cos a cosec 0) do -(1-cos a). 2 ||

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Q: ( sin(3x+1) cos?(3x+1) Evaluate

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Q: Rewrite – 4 sin(x) – 5 cos(x) as A sin(x + ø) A = $ =

A: Given the trigonometry function

Q: The function f(x) = x+ O Even O Odd x+cos (5 €) is O None of the above

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Q: Find the exact value of 1 - O sin(√2) O cos(√2) cos(2) O ln(1 + √2) O e ² 2 2! +4 8 6! + 16 8! 32…

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Q: Prove the identity: sin(0)-co sin (0) +cos (0)–1 cos (8)+1 sin(0)+1 cos(8)

A: On proving this we will get

Q: Prove the identity 28in CA+ )•cos (A+ ) = 2 cos A-1 %3D

A: We have to verify the identity: 2sinA+π4·cosA+π4=2cos2A-1 Here we are going to use these identities:…

Q: Evaluate A2 (sin x) O A. sin(x + 2h) – sin(x + h) + 2 sin x O B. sin(x + h) – sin x O C. sin(x + 2h)…

A: We  need to evaluate ∆2(sinx) The solution is explained below.