Class 12
MATHS
Trigonometric Functions

# If (secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB)(secC-tanC), prove that value of each side is pm1.

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Text Solution

Solution :
Let <br> (secA+tanA)(secB+tanB)(secC+tanC)=x (i) <br> :. (secA-tanA)(secB-tanB)(secC-tanC)=x (ii) <br> Multiplying Eqs.(i) and (ii), we get <br> (sec^2A-tan^2A)(sec^2B-tan^2B)(sex^2C-tan^2C)=x^2 <br> or x^2=1 <br> :. x=pm1 <br> Hence, each side is equal to pm1.

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