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Evaluate the following (i) sin 60^@ co...

Evaluate the following
(i) `sin 60^@ cos30^@ + sin 30^@ cos 60^@`
(ii) `2tan^2 45^@ + cos^2 30^@ - sin^2 60^@`
(iii) `(cos45^@)/(sec30^@ + c o s e c 30^@)`
(iv) `(sin30^@ + tan45^@ - c o s e c 60^@ )/(sec30^@ + cos60^@ +cot45^@)`
(v) `(5cos^2 60^@ + 4sec^2 30^@ - tan^2 45^@ )/ (sin^2 30^@ + cos^2 30^@ ) `

Text Solution

Verified by Experts

(i) `sin60^@cos30^@ + sin30^@cos60^@`
`=sin(60^@+30^@) = sin90^@ = 1`

(ii)`2tan^2 45^@ +cos^2 30^@ - sin^2 60^@`
`=2(1)^2 +(sqrt3/2)^2 - (sqrt3/2)^2`
`=2`

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Knowledge Check

  • The value of (4cos^2 60^@ + 3 sec^2 30^@ -cot^2 45^@)/(cos^2 60^@ + sin^2 60^@) is:

    A
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    B
    4
    C
    6
    D
    5

  • The value of cos^2 30^@ + sin^2 60^@ + tan^2 45^@ + sec^2 60^@ + cos 0^@ is

    A
    `4 1/2`
    B
    `5 (1)/(2)`
    C
    `6 (1)/(2)`
    D
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  • Evaluate : ( 5 cos ^(2) 60^(@) + 4 sec^(2) 30^(@) - tan^(2) 45^(@))/( sin^(2) 30^(@) + cos^(2) 30^(@))

    A
    `2 (5)/(16)`
    B
    `(67)/(12)`
    C
    0
    D
    1

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