Home
Class 11
MATHS
Prove that 2sin^2(pi/6)+cosec^2((7pi)/6)...

Prove that `2sin^2(pi/6)+cosec^2((7pi)/6)cos^2(pi/3)=3/2`

Text Solution

Verified by Experts

(cosec) (7 pi)/(6)=(cosec)(210)^(0)=(cosec)(180+30)^(0)=-(cosec) 30^(circ)=-2. .cos ((pi)/(3)) equiv (1)/(2), sin (pi)/(6)=(1)/(2) - .. .2 sin ^(2) (pi)/(6)+(cosec)^(2) (7 pi)/(6_(2)) cos ^(2), (pi)/(3)=2 xx((1)/(2))^(2)+(-2)^(2) xx((1)/(2))^(2)=2 xx (1)/(4)+4 xx (1)/(4)=(1)/(2)+1=(3)/(2).
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    V PUBLICATION|Exercise QUESTIONBANK|99 Videos

Similar Questions

Explore conceptually related problems

Prove that 2sin^2((3pi)/4)+2cos^2(pi/4)+2sec^2(pi/3)=10

Prove that cot^2(pi/6)+cosec((5pi)/6)+3tan^2(pi/6)=6

Prove that sin^2(pi/6)+cos^2(pi/3)-tan^2(pi/4)=-1/2

Find the value of the following: 2sin^2(pi/6)+cosec^2((7pi)/3)cos((2pi)/3)

Prove that 3sin(pi/6)sec(pi/3)-4sin((5pi)/6)cot(pi/4) =1

Prove that sin^2(pi/8)+sin^2((3pi)/8)+sin^2((5pi)/8)+sin^2((7pi)/8)=2

Show that 2sin^2 (pi/6)+sin^2 (pi/4)=1

Evaluate cos^2(pi/8)+cos^2((3pi)/8)

Prove that 2cos(pi/13)cos((9pi)/13)+cos((3pi)/13)+cos((5pi)/13)=0

Prove that tan^2frac(pi)(4)+sin^2frac(pi)(6)-cos^2frac(pi)(3)=1