UPSKILL MATH PLUS

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1. If \(sin \ \theta = \frac{a}{\sqrt{a^2 + b^2}}\), then show that \(b sin \ \theta = a cos \ \theta\).
 
Proof:
 
LHS: \(b sin \ \theta =\) iiii+ii
 
RHS: \(a cos \ \theta =\) iiii+ii
 
Since LHS \(=\) RHS, then \(b sin \ \theta = a cos \ \theta\).
 
Hence, we proved.
 
(Note: Enter the letters in alphabetical order.)
 
2. If \(3 cot \ A = 2\), then find the value of \(\frac{4 sin \ A - 3 cos \ A}{2 sin \ A + 3 cos \ A}\).
 
Answer:
 
\(\frac{4 sin \ A - 3 cos \ A}{2 sin \ A + 3 cos \ A} =\) ii