If A+B+C=90° and cosA=cosB×cosC then show that tanB +tanC= 1

Asked by akankshibhattacharjee4 | 24th May, 2014, 02:00: PM

Expert Answer:

G i v e n space t h a t space A plus B plus C equals 90 degree space a n d space cos A equals cos B cross times cos C W e space n e e d space t o space p r o v e space t h a t space tan B plus tan C equals 1 S i n c e space A plus B plus C equals 90 degree rightwards double arrow B plus C equals 90 degree minus A N o w space co n s i d e r space tan B plus tan C : tan B plus tan C equals fraction numerator sin B over denominator cos B end fraction plus fraction numerator sin C over denominator cos C end fraction rightwards double arrow tan B plus tan C equals fraction numerator sin B cos C plus sin C cos B over denominator cos B cos C end fraction rightwards double arrow tan B plus tan C equals fraction numerator sin open parentheses B plus C close parentheses over denominator cos B cos C end fraction rightwards double arrow tan B plus tan C equals fraction numerator sin open parentheses 90 degree minus A close parentheses over denominator cos B cos C end fraction rightwards double arrow tan B plus tan C equals fraction numerator cos A over denominator cos B cos C end fraction rightwards double arrow tan B plus tan C equals fraction numerator cos A over denominator cos A end fraction rightwards double arrow tan B plus tan C equals 1

Answered by Vimala Ramamurthy | 26th May, 2014, 11:39: AM