+91-87964 74404
FlagBACK
Question icon
Grade 10Trigonometry

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

Profile image of Ananya
8 Years agoGrade 10
Answers icon

1 Answer

Profile image of Soumendu Majumdar
ApprovedApproved Tutor Answer8 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!

Other Related Questions on trigonometry

question mark
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available

Last Activity: 3 Years ago

question mark
  • Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
1 Answer Available

Last Activity: 4 Years ago

question mark
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
1 Answer Available

Last Activity: 4 Years ago

question mark
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
1 Answer Available

Last Activity: 4 Years ago

question mark
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥 
trigonometry
1 Answer Available

Last Activity: 4 Years ago