Question

If 3sin@ - 4cos@ = 0 then find the value of tan@, sec@, cosec@, where @ is an acute angle.
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Answer 1

Answer:

Step-by-step explanation:

3sinβ - 4cosβ = 0 ( 0° < β < 90° )

3sinβ = 4cosβ

$\frac{sin\beta }{cos\beta }$ = $\frac{4}{3}$

tanβ = $\frac{4}{3}$

sec²β = 1 + tan²β ⇒ secβ = $\sqrt{1+tan^2 \beta }$

secβ = $\sqrt{\frac{25}{9} }$ = $\frac{5}{3}$

csc²β = 1 + cot²β

cotβ = $\frac{1}{tan\beta }$ = $\frac{3}{4}$

csc²β = 1 + (  $\frac{3}{4}$ )² = $\frac{25}{16}$

cscβ = $\frac{5}{4}$