Trigonometry

cos(a+b)=4/5 &cps(a-b)=5/13 & a,b lies in b/w 0^o to 45^o ,find the value of tan2a.

2 Answers

tan(2a)=tan(a+b+a-b)
= tan(a+b)+ tan(a-b)/1-tan(a+b)tan(a-b)
find value of tan(a+b) and tan(a-b)

ans is -63/16

sin { a + b } = 3 / 5

Hence , tan { a + b } = 3 / 4 ...................... [ these can be easily found out ]

sin { a - b } = 12 / 13

Hence , tan { a - b } = 12 / 5 ..................... [ proceeding in the similar way ]

So , tan { 2 a } = tan { a + b + a - b }

= tan [ { a + b } + { a - b } ]

= tan { a + b } + tan { a - b }1 - tan { a + b } tan { a - b }

= 3 / 4 + 12 / 51 - { 36 / 20 }

= - 6316

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