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Grade 12Trigonometry

prove that cos^-1(4/5)+sin^-1(3/√34)=tan^-1(27/11)
prove that cos^-1(4/5)+sin^-1(3/√34)=tan^-1(27/11)prove that cos^-1(4/5)+sin^-1(3/√34)=tan^-1(27/11)prove that cos^-1(4/5)+sin^-1(3/√34)=tan^-1(27/11)

Profile image of KATTA VIJAYA MOUNIKA (S170106)
7 Years agoGrade 12
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1 Answer

Profile image of Arun
7 Years ago
Note that taking a 3,4,5- right triangle, 

sin^-1( 3/sqrt34) = tan^-1( 3/5). 
cos^-1 ( 4/5) = tan^-1 (3/4)
Now 

tan^-1 a + tan^-1 b = tan^-1[ ( a + b )/ ( 1 - ab ) ]. 

Hence, LHS = 

tan^-1 ( 3/5) + tan^-1 ( 3/4) 

= tan^-1 [ ( 3/5 + 3/4 ) / ( 1 - 3/5.3/4 ) ]
 
= tan^-1 [27/11]