tmua 2022 Q9

tmua · Uk · paper1 1 marks Trig Proofs Extremal Value of Trigonometric Expression

This question is about pairs of functions f and g that satisfy
$$\begin{aligned} f ( x ) - g ( x ) & = 2 \sin x \\ f ( x ) g ( x ) & = \cos ^ { 2 } x \end{aligned}$$
for all real numbers $x$.
Across all solutions for $\mathrm { f } ( x )$, what is the minimum value that $\mathrm { f } ( x )$ attains for any $x$ ?

..... 11

This question is about pairs of functions f and g that satisfy

$$\begin{aligned}
f ( x ) - g ( x ) & = 2 \sin x \\
f ( x ) g ( x ) & = \cos ^ { 2 } x
\end{aligned}$$

for all real numbers $x$.

Across all solutions for $\mathrm { f } ( x )$, what is the minimum value that $\mathrm { f } ( x )$ attains for any $x$ ?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20