Question

Cos(alpha-beta)=3/5 sin(alpha+beta)=5/13 then tan 2 alpha

Answer 1

Answer:

tan 2α =21/4

Step-by-step explanation:

cos(α-β)=3/5

sin(α+β)=5/13

Let  α-β=x and α+β=y

cos x=3/5 so sec x=5/3

sec²x-tan²x=1

(5/3)²-tan²x=1

tan²x=(5/3)²-1=25/9-1=16/9

tanx=4/3

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similarly

cot²y=cosec²y-1

=169/25-1

=(169-25)/25

tan²y=144/25

coty =12/5

tany=5/12

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tan(x+y)=( tanx+tany)/ ( 1-tanxtany)

=(4/3+5/12) /(1-4/3*5/12)

=(16+5/5) /(1-5/9)

=21/5 / 4/5

=21/5 *5/4

tan(x+y)=21/4

tan (α-β+α+β)=21/4

tan 2α =21/4