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Prove that tan 75+cot 75=4 using compund angle formula

Prove that tan 75+cot 75=4 using compund angle formula

Grade:10

1 Answers

Soumendu Majumdar
159 Points
5 years ago
Dear Student,
tan 75^{\circ} + cot 75^{\circ} = sec 75^{\circ}cosec75^{\circ}
so sin75^{\circ}=sin(45^{\circ}+30^{\circ}) =sin45^{\circ}cos30^{\circ} +cos45^{\circ}sin30^{\circ}   since sin(A+B)=sinAcosB + sinBcosA
=(\sqrt{3}+1)/2\sqrt{2}
cos75^{\circ}=cos(45^{\circ}+30^{\circ})=cos45^{\circ}cos30^{\circ} - sin45^{\circ}sin30^{\circ}   since cos(A+B)=cosAcosB – sinAsinB
=(\sqrt{3}-1)/2\sqrt{2}
Now sec75^{\circ}cose75^{\circ}=1/sin75^{\circ}cos75^{\circ}
=(2\sqrt2 )^2/(\sqrt3+1)(\sqrt3-1)
=8/2
= 4
Hope it helps!

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