Question

write the expression for
1) Sin 2 A
2)Cos 2 A
3) Tan 2 A

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Answer 1

Answer:

1) 2sinAcosA

2)cos^2A-sin^2A

3)2tanA/(1-tan^2A

Step-by-step explanation:

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Answer 2

$\sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2 \tan( \alpha ) }{1 + { \tan^{2}( \alpha ) } }\ \\ \\ \cos(2 \alpha ) = \cos ^{2} ( \alpha ) - \sin^{2} ( \alpha ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {2 } cos ^{2} ( \alpha ) - 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 - {2 } \sin^{2}( \alpha ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \ \frac{1 - \tan ^{2} ( \alpha ) }{1 + \tan ^{2} ( \alpha )} \\ \\ \tan(2 \alpha ) = \frac{2 \tan( \alpha ) }{1 - { \tan^{2}( \alpha ) } }$