Question

3 tan2 45° - sin2 60°-1/2cot2 30°+1/8sec2 45°


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Answer 1

3tan2 45 -sin2 60 - 1/2 cot2 30 + 1/8 sec2 45

3 x 1 - 3/4 - 1/2 x 3 + 1/8 x 4

3 - 3/4 - 3/2 + 4/8

3 - 3/4 - 3/2 + 1/2

12 - 3 - 6 + 2 / 4

14 - 9 /4

5/4 ans

Answer 2

$\underline{\boxed{\bold{Question}}}$

• Evaluate : E = 3tan²45° - sin²60° - 1/2(cot²30°) + 1/8 (sec²45°)

$\underline{\boxed{\bold{Things \; to \; be \; remembered}}}$

• Values of trigonometric function of some standard angle given in attachment

$\underline{\boxed{\bold{Answer}}}$

→ 3tan²45°            = 3 × (1)² = 3

→ sin²60°              = {(√3)/2}² = 3/4

→ 1/2(cot²30°)       = 1/2 × (√3)² = 3/2

→ 1/8 (sec²45°)      = 1/8 × (√2)² = 1/4

∴ Now lets substitute values in the given expression

E = 3tan²45° - sin²60° - 1/2(cot²30°) + 1/8 (sec²45°)

  = 3 - 3/4 - 3/2 + 1/4

  = 3 -2/4 - 3/2

  = 3 -1/2 - 3/2

  = 3 - 4/2

  = 3 - 2

 = 1

$\underline{\boxed{\bold{\therefore Value \; of \; expression \;E = 1}}}$

Hope this helps u..../

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