Question

Without using trigonometric tables find the value of 3sin^2(45°)+2 cos^2(60°).

Answer 1

Answer:

$i)Value \: of \: 3sin^{2} 45\degree + 2 cos^{2} 60\degree$

$= 3 \times \left( \frac{1}{\sqrt{2}}\right)^{2} + 2 \times \left( \frac{1}{2}\right)^{2}$

$= 3 \times \frac{1}{2} + 2 \times \frac{1}{4}\\= \frac{3}{2} + \frac{1}{2}\\= \frac{ 4}{2} = 2$

Therefore.,

$\red {Value \: of \: 3sin^{2} 45\degree + 2 cos^{2} 60\degree}\green {= 2}$

$ii) Given \: log _{10}x = a \implies x = 10^{a}$

$log _{10}y = b \implies y = 10^{b}$

$log _{10}z = 3a - 2b \implies z = 10^{3a-2b}$

$\implies z = \frac{10^{3a}}{10^{2b}}\\= \frac{ (10^{a})^{3}}{(10^{b})^{2}}\\= \frac{x^{3}}{y^{2}}$

Therefore.,

$\red {z} \green {= \frac{x^{3}}{y^{2}}}$

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