Q30 of 40 Page 1

Prove that (1 + tan A – sec A) × (1 + tan A + sec A) = 2 tan A

OR


Prove that


Taking LHS

(1 + tan A – sec A)(1 + tan A + sec A)


Using (a – b)(a + b) = a2 – b2


= (1 + tan A)2 – sec2A


= 1 + tan2A + 2 tan A – sec2A


= sec2A + 2 tan A – sec2A


= 2 tan A


= RHS


OR


Taking LHS







= 2 sec2θ


= RHS


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28

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OR


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 31

Given that √3 is an irrational number, show that (5+2√3) is an irrational number.

OR


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 32

Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.