Prove that sin 34 - sin 56-cos 34 - cos 56- 34-cosec 34

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Mathematics

Standard Values of Trigonometric Ratios

Prove that si...

Question

Prove that sin 34/sin 56+cos 34/cos 56= sec34*cosec34

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Solution

LHS

Sin34/Sin56 + Cos 34/Cos56

= Sin(90-56)/Sin56 + Cos(90-56)/Cos56

= Cos56/Sin56 + Sin56/Cos56

= { Cos ^(2) 56 + Sin ^(2) 56 } / { Sin56 × Cos56 }

= 1 / Sin56 × Cos56

= 1 / { Sin(90 - 34) × Cos(90 - 34) }

= 1 / Cos34 × Sin 34

= Sec34 × Cosec 34

= RHS

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