If A-tan A B-tan B C-tan C- A-tan A B-tan B C-tan C- then each side is equal to

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Standard XII

Mathematics

Algebra of Derivatives

If A+tan A B+...

Question

If (sec A + tan A)(sec B + tan B)(sec C + tan C) = (sec A - tan A)(sec B - tan B)(sec C - tan C), then each side is equal to

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Solution

The correct option is A 1
(a,b) If L=M, then L $^{2}$ = LM or ML = M $^{2}$
Both LM = ML = 1 as sec $^{2}$ A - tan $^{2}$ A = 1
$∴$ L $^{2}$ = M $^{2}$ = 1.

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If (sec A + tan A)(sec B + tan B)(sec C + tan C) = (sec A - tan A)(sec B - tan B)(sec C - tan C), then each side is equal to

The correct option is A 1(a,b) If L=M, then L2 = LM or ML = M2 Both LM = ML = 1 as sec2A - tan2A = 1 ∴L2 = M2 = 1.

The correct option is A 1
(a,b) If L=M, then L $^{2}$ = LM or ML = M $^{2}$
Both LM = ML = 1 as sec $^{2}$ A - tan $^{2}$ A = 1
$∴$ L $^{2}$ = M $^{2}$ = 1.