Question

sin^2120°+cos^2150°+tan^2120+cos^2180°-tan135°=9/2 show it
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Answer 1

sin²120°+cos²150°+tan²120°+cos²180°-tan135° = 9/2 is proved.

Step-by-step explanation:

To Prove :

sin²120°+cos²150°+tan²120°+cos²180°-tan135° = 9/2

Proof:

L.H.S

sin 120 ° = √3/2

cos 150° = -√3/2

tan 120° = -√3

cos 180° = -1

tan 135° = -1

By substituting the corresponding values we get,

∴$(\frac{\sqrt{3} }{2}) ^{2}+(-(\frac{\sqrt{3} }{2}) ^{2}+(-\sqrt{3})^2+(-1)-(-1)$

= $\frac{3}{4} +\frac{3}{4} +3-1+1$

= $\frac{3+3+12-4+4}{4}$

= $\frac{18}{4} = 4.5$

R.H.S

$\frac{9}{2}= 4.5$

Hence L.H.S = R.H.S

To Learn More.....

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