PRE-CALCULUS/TRIG 3
𝑠𝑖𝑛2𝑥 = 2𝑠𝑖𝑛𝑥𝑐𝑜𝑠𝑥
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𝑐𝑜𝑠2𝑥 = 𝑐𝑜𝑠 2 𝑥 − 𝑠𝑖𝑛2 𝑥
= 2𝑐𝑜𝑠 2 𝑥 − 1
= 1 − 2𝑠𝑖𝑛2 𝑥
2𝑡𝑎𝑛𝑥
𝑡𝑎𝑛2𝑥 = 1−𝑡𝑎𝑛2 𝑥
Examples:
3
1) If sin x= 4 in Quadrant I, find each of the double angle values.
a) sin 2x=
2) If cos x=
−24
25
a) sin 2x=
b) cos 2x=
c) tan 2x=
in Quadrant III, find each of the double angle values.
b) cos 2x=
c) tan 2x=
Verifying Identities Double Angle Formulas
EXAMPLES:
1) cos 4 x − sin4 x = cos2x
2) sin2x = −2sinxsin(x − 90°)