5253 A sin 7x cos 6x cos 7x sin 6x SolutionA sinAcosBcosAsi

5.2/5.3

A)

sin 7x cos 6x + cos 7x sin 6x

Solution

A) sinAcosB+cosAsinB=sin(A+B)

sin7x cos6x +cos7xsin6x

=sin(7x+6x)

=sin(13x)

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B)2tanA_/(1-tan²A)=tan2A

tan67.5^o_{/(1-tan²67.5^o)}

=(1_/2) 2tan67.5^o_{/(1-tan²67.5^o)}

=(1_/2)tan(2*67.5^o)

=(1_/2)tan(135^o)

=(1_/2)(-1)

=(-1_/2)

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C)tan=15_/8

sin=15/[15²+8²] =15/17 ,cos=8/[15²+8²] =8/17

sec2

=1_/cos2

=1_{/(cos²-sin²)}

=1_{/((8/17)²-(15/17)²)}

=1_{/((64/289)-(225/289))}

=1/(-161/289)

=-289/161

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D)csct =5

sint=1_/5

sec2t

=1_/cos2t

=1_/(1-2sin²t)

=1_{/(1-2(1/5)²)}

=1_/(1-(2/5))

=1_/(3/5)

=5_/3