cos beta =1/5
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Answer:
Beta = cos^-1 (1/5)
Step-by-step explanation:
Explanation - taking inverse of a function
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Given 3sinβ+5cosβ=5, then the value of (3cosβ−5sinβ)
2
is
Medium
Solution
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Correct option is A)
3sinβ+5cosβ=5
5cosβ=5−3sinβ
Squaring both the sides we get
25cos
2
β=25+9sin
2
β−30sinβ
30sinβ=34sin
2
β
Therefore
34
30
=sinβ ...(i)
Hence cosβ=
1−sin
2
β
=
34
16
...(ii)
Substituting in the expression the values of sinβ and cosβ
Therefore
(3cosβ−5sinβ)
2
=(
34
(3)16
−
34
(5)30
)
2
=(
34
48−150
)
2
=(
34
−102
)
2
=(−3)
2
=9
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