Question

can someone check if i answered these 2 right?

Which are identities (check all that apply) :

cos^2 3x - sin^2 3x = cos6x

(sinx + cosx)^2 = 1 + sin2x

sin^6 x + cos^6 x = 4 - 3sin^2 2x

sinx + sin5x = tan3x

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Which of the following are identities (check all that apply :

cos(x + y) + cos(x - y) = cos^2 x - sin^2 y

sin(x + y) - sin(x - y) = 2cosx siny

cos(x + y) + cos(x - y) = 2cosx cosy

sin(x - pi) = - sinx

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for question 1 I have the 1st and 2nd choices
& for 2nd question: 1st &3rd

Answer 1

You're correct on the first question.

For the second question, it's impossible for the 1st and 3rd choices to both be identities since (cosx)^2-(siny)^2 =/= 2cosx cosy, but both are said to equal the same thing. Instead, all of the choices are true except for the 1st.

To show that they are identities, you need to expand the expressions on the left using the trig formulas for sum/difference of angles.

Answer 2

ohhh okay! thank you so much! i think i see what i did wrong on the 2nd one