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प्रश्न
What will be the value of sin 45° + `1/sqrt(2)`?
विकल्प
`1 + sqrt(2)`
`2sqrt(2)`
`1/sqrt(2)`
`sqrt(2)`
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उत्तर
`sqrt(2)`
Explanation:
sin 45° + `1/sqrt(2) = 1/sqrt(2) + 1/sqrt(2)` .....`[∵ sin^circ = 1/sqrt(2)]`
= `(1 + 1)/sqrt(2)`
= `2/sqrt(2)`
= `2/sqrt(2) xx sqrt(2)/sqrt(2)`
= `(2sqrt(2))/2`
= `sqrt(2)`
Thus, the value of sin 45° + `1/sqrt(2)` is `sqrt(2)`.
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संबंधित प्रश्न
State whether the following are true or false. Justify your answer.
sec A = `12/5` for some value of angle A.
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Evaluate the following:
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following:
cos 60° cos 45° – sin 60° sin 45°
Evaluate the following:
`cot^2 30^@ - 2 cos^2 60^circ- 3/4 sec^2 45^@ - 4 sec^2 30^@`
Evaluate the following:
(cos 0° + sin 45° + sin 30°)(sin 90° – cos 45° + cos 60°)
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Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
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