Prove trigonometric identity and how to have ideas This is the identity: cos 2 </msu

Jamison Rios 2022-07-02 Answered
Prove trigonometric identity and how to have ideas
This is the identity:
cos 2 ( a ) cos 2 ( b ) = tan 2 ( b ) tan 2 ( a ) ( 1 + tan 2 ( a ) ) ( 1 + tan 2 ( b ) )
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Answers (1)

earendil666h1
Answered 2022-07-03 Author has 10 answers
Starting from the Pythagorean Theorem:
c o s 2 x + s i n 2 x = 1
Then dividing this by c o s 2 x we have:
1 + t a n 2 x = s e c 2 x
Now let's look at the LHS:
c o s 2 a c o s 2 b = c o s 2 a c o s 2 b ( 1 c o s 2 b 1 c o s 2 a )
= 1 s e c 2 a s e c 2 b ( s e c 2 b s e c 2 a )
From earlier we know how to substitute s e c 2 x and have
= 1 ( 1 + t a n 2 a ) ( 1 + t a n 2 b ) ( 1 + t a n 2 b ) ( 1 + t a n 2 a )
Or simplified:
t a n 2 b t a n 2 a ( 1 + t a n 2 a ) ( 1 + t a n 2 b )
The identities often revert back to P.T. at some point and is often a good place to start.
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