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if tan theta = 1/7 and tan phi= 1/3 then prove that cos 2 theta= sin 4 phi

3 answers

tanθ=1/7 means sinθ=1/√50
cos 2θ = 1-2sin^2θ = 1-1/25 = 24/25

tanØ=1/3 means sinØ=1/√10 and cosØ=3/√10
sin2Ø = 2sinØcosØ = 3/5
so, cos2Ø = 4/5
sin4Ø = 2sin2Øcos2Ø = 24/25
tanθ=1/7 means sinθ=1/√50
cos 2θ = 1-2sin^2θ = 1-1/25 = 24/25

tanØ=1/3 means sinØ=1/√10 and cosØ=3/√10
sin2Ø = 2sinØcosØ = 3/5
so, cos2Ø = 4/5
sin4Ø = 2sin2Øcos2Ø = 24/25
tanθ=1/7 means sinθ=1/√50
cos 2θ = 1-2sin^2θ = 1-1/25 = 24/25

tanØ=1/3 means sinØ=1/√10 and cosØ=3/√10
sin2Ø = 2sinØcosØ = 3/5
so, cos2Ø = 4/5
sin4Ø = 2sin2Øcos2Ø = 24/25
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