Question

find the value of tan 10°.tan 25° + tan 25°.tan 55°+ tan 55°.tan 10°=​

Answer 1

Answer:

we know, 25 +10+55 = 90

or, 25 + 10 = 90 -55

Taking tan on both sides, then

or, tan ( 25+10) = tan ( 90-55)

or,( tan 25 + tan 10 ) / ( 1-tan 25 * tan 10 ) = cot 55  

or, ( tan 25 + tan 10 ) / ( 1-tan 25 * tan 10 ) =  1 / tan 55

or, ( tan 25 + tan 10 ) * tan 55 = ( 1-tan 25 * tan 10 )

or, tan 25 * tan 55 + tan 55 *tan 10 = 1 - tan 25 *tan 10

---> tan 10°.tan 25° + tan 25°.tan 55°+ tan 55°.tan 10°=​  1

Hence, the value is 1

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