which of the following are identities? check all that apply. A. (sinx + cosx)^2= 1+sin2x B. sin6x=2 sin3x cos3x C. sin3x/

Question

which of the following are identities? check all that apply.
A. (sinx + cosx)^2= 1+sin2x
B. sin6x=2 sin3x cos3x
C. sin3x/sinxcosx = 4cosx – secx
D. sin3x-sinx/cos3x+cosx = tanx

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bonexptip 5 years 2021-07-30T11:37:01+00:00 2 Answers 239 views 0

Answers ( )

  1. quangkhai
    -1
    2021-07-30T11:38:25+00:00
    Reply

    Answer:

    Option A and B.

    Step-by-step explanation:

    A.

    (Sin x + Cos x)^2 = sin^2 x + cos^2 x + 2 sin x cos x = 1 + sin 2 x

    So, it is an identity.

    B.

    Sin 6 x = 2 sin 3x cos 3x

    Here, sin 2 A = 2 Sin A cos A is used , so it is an identity.

    C. sin3x/sinxcosx = 4cosx – secx

    It is not an identity.  

    D. sin3x-sinx/cos3x+cosx = tanx

    It is not an identity.

  2. Giakhanh
    1
    2021-07-30T11:38:30+00:00
    Reply

    Answer: (a), (b), (c), and (d)

    Step-by-step explanation:

    Check the options

    (a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x

    (b)\\\Rightarrow \sin (6x)=\sin 2(3x)\\\Rightarrow \sin 2(3x)=2\sin (3x)\cos (3x)

    (c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x

    (d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x

    Thus, all the identities are correct.

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