Question

2 sin square 5 by 6 + cos square 756 cos square pi by 3 equal to 3 by 2 ​

Answer 1

Hi there,

I think there is some incorrect values given in the question. Also, with cos square 7pi/6 the afinal answer does not match the RHS, so in order to match 3/2 it should be cosec square 7pi/6. I have rewritten the correct question and solved it accordingly. Thanks

Q. 2 sin square pi/6 + cosec square 7pi/6 cos square pi/3 equal to 3 by 2.

2 sin square pi by 6 + cosec square 7pi/6 cos square pi by 3 is proved to be equal to 3 by 2.

Step-by-step explanation:

Required formulas:

(i) sin π/6 = sin 30° = 1/2

(ii) cosec 7π/6 = cosec (π + π/6) = cosec (-π/6) = - cosec 30° = - 2 …… [since cosec θ = 1/sin θ and sin function is negative in the third quadrant]

(iii) cos π/3 = cos 60° = ½

Now, taking L.H.S.

2 sin² (π/6) + cosec² (7π/6) * cos² (π/3)

= 2 [½]² + [{-2}² * {½}²]

= [2 * ¼] + [4 * 1/4]

= ½ + 1

= [2+1]/2

= 3/2

= R.H.S

Hence proved

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Answer 2

Answer:

Step-by-step explanation:

Given  

2 sin square  π  by 6 + cos square 7 π/6 cos square pi by 3 equal to 3 by 2  

    2 sin ^2 π / 6 + cosec^2 7π / 6 cos^2 π / 3

    2 sin^2 30 + cosec^2 210 cos^2 60

    2 sin^2 30 + 1/sin^2 210 cos^2 60

    2 x (1/2)^2 + 1/ 1/(-1/2) ^2 (1/2 )^2

     2 x 1/4 + 4 x 1/4

      1/2 + 1

   = 3/2 proved