Answer:
True
Step-by-step explanation:
sec = 1/cos
tan = sin/cos
sec/tan = 1/sin
1/sin != sin
1/sin 45 != sin 45
!= means not equal in programming languages
An expression is defined as a set of numbers, variables, and mathematical operations. The counterexample for the expression secθ/tanθ=sinθ is 45 degrees is false.
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified as,
secθ / tanθ
= (1/cosθ)/ (sinθ/cosθ)
= 1/ sinθ
Substitute the value of θ as 45°,
= 1/(sin 45°)
= 1/ (1/√2)
= √2
The value of secθ/tanθ when θ=45° is √2, while the value of sinθ when θ=45° is 1/√2.
Hence, the counterexample for the expression secθ/tanθ=sinθ is 45 degrees is false.
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