1800-150-456-789
FlagBACK
Flag Trigonometry> Prove that tan 75+cot 75=4 using compund ...
question mark

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

Ananya , 6 Years ago
Grade 10
anser 1 Answers
Soumendu Majumdar

Last Activity: 6 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!

Provide a better Answer & Earn Cool Goodies

Enter text here...
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Enter text here...

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: 2 Years ago

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

Last Activity: 2 Years ago

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

Last Activity: 2 Years ago

question mark
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
trigonometry
0 Answer Available

Last Activity: 2 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
0 Answer Available

Last Activity: 2 Years ago