Question

evaluate: Tan^2 30 . Sin 30 +cos 60.sin^2 90. Tan 60 -2 tan 45 . Cos^2 0 . Sin 90

Answer 1

Answer:

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Answer 2

The value of the expression is [3√3 - 11 ]/6

Given:

Tan² 30 × Sin 30 +cos 60 × sin² 90 × Tan 60 -2 tan 45 × Cos² 0 × Sin 90

To find:

Evaluate the above equation

Solution:

From the trigonometric ratio table:

Angle Sin  Cos     Tan

0°         0    1        0

30°   1/2 √3/2     1/√3

45°         1/√2    1√2        1

60°        √3/2     1/2      √3

90°      1      0     Undefined

Now use above values to evaluate the expression

=> Tan² 30 ×Sin 30 +cos 60 × sin² 90 ×Tan 60 - 2 tan45 ×Cos² 0 × Sin 90

On substituting value we get

=> (1/√3)² ×(1/2) +(1/2) ×(1)² ×(√3) - 2 (1) ×(1)² × 1

=> (1/6) + √3/2 - 2  

=> [ 1 + 3√3 - 12]/6      [ Take 6 as LCM ]

=> [3√3 - 11 ]/6

Therefore,

The value of the expression is [3√3 - 11 ]/6

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