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$80 . If \cot θ = \frac{12}{5}, show that \tan^{2} θ - \sin^{2} θ = \sin^{4} θ \sec^{2} θ .$

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80   If   cot   θ = 12 5 ,   show  
that   tan 2   θ - sin 2   θ = sin 4
  θ   sec 2   θ

Neha Sethi · Accepted Answer

Dear student
Given: cotθ=125=BPBy pythagoras theorem, we haveH2=P2+B2    , where P=Perpendicular,B=base,H=hypotenuse
H2=52+122H2=25+144H2=169H=13 units
Now, tanθ=PB=512sinθ=PH=513secθ=HB=1312Consider LHStan2θ-sin2θ=5122-5132=25144-25169=4225-360024336=62524336  
1Consider RHSsin4θ sec2θ=5134×13122=625169×144=62524336  
2From 1 and 2RHS=LHSHence Proved
Regards

Solve this : Please don't send any links 80 . If cot θ = 12 5 , show that tan 2 θ - sin 2 θ = sin 4 θ sec 2 θ .

Solve this : Please don't send any links

$80 . If \cot θ = \frac{12}{5}, show that \tan^{2} θ - \sin^{2} θ = \sin^{4} θ \sec^{2} θ .$