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secondary 4 | A Maths
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How to prove this identity?
Thank you for helping me!!
Date Posted: 3 years ago
Views: 371
sin 2x = 2 sin x cos x (recall the double angle formula for sine)
= 2 sin x cos x × 1
= 2 sin x cos x × cos x / cos x
(Introduce a cos x into the numerator to obtain cos² x, which can be converted to in terms of cos 2x later.
We also introduce cos x into the denominator so as to create a tan x)
= 2 sin x cos² x / cos x
= (sin x / cos x)(2 cos² x)
= tan x (1 + cos 2x)
(proved)
(Recall the double angle formula for cosine :
cos 2A = cos² A - sin² A = 2 cos²A - 1 = 1 - 2 sin²A
So, 2 cos² A = 1 + cos 2A)
= 2 sin x cos x × 1
= 2 sin x cos x × cos x / cos x
(Introduce a cos x into the numerator to obtain cos² x, which can be converted to in terms of cos 2x later.
We also introduce cos x into the denominator so as to create a tan x)
= 2 sin x cos² x / cos x
= (sin x / cos x)(2 cos² x)
= tan x (1 + cos 2x)
(proved)
(Recall the double angle formula for cosine :
cos 2A = cos² A - sin² A = 2 cos²A - 1 = 1 - 2 sin²A
So, 2 cos² A = 1 + cos 2A)
See 1 Answer
Hi again, check your question's comments section for the working
Tysm for the clear step-by-step explanation~ i got it now
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