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If tan(45+a)+tan(45_a)=p then tan^2(45+a)+tan^2(45_a)=?

If tan(45+a)+tan(45_a)=p then tan^2(45+a)+tan^2(45_a)=?

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
tan (45 +A) = tan 45 + tanA/ 1 - tan45 tanA = (1 + tanA) /(1 - tanA)
Similarly
tan(45 -A) = (1 - tanA) /(1 + tanA)
 
Hence
tan (45 -a) tan(45 +a) = 1
 
Now
Square both the sides of given equation
Tan²(45 +a) + tan²(45 -a) + 2 tan(45+a) tan(45-a) = p²
Tan2(45 +a) + tan² (45 -a) = p² -2
 
Which is the required answer.
 
Regards
Arun (askIITians forum expert)

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