Trigonometry

The equation $cos ^{2} theta=frac{(x+y)^{2}}{4 x y}$  is only possible when ? A. x = -y B. x > y C. x = y D. x < y Answer: Option C Show Answer Solution(By Apex Team) $begin{array}{l}cos^2theta=frac{(x+y)^2}{4xy}\ text{Max value of cos}^2theta=1\ begin{array}{l} Rightarrow 1=frac{(x+y)^{2}}{4 x y} \ Rightarrow 4 x y=(x+y)^{2} \ Rightarrow 4...

The greatest value of $sin ^{4} theta+cos ^{4} theta$ is. A. 2 B. 3 C. $frac{1}{2}$ D. 1 Answer: Option D Show Answer Solution(By Apex Team)   $begin{array}{l}sin^2theta+cos^2theta=1\ text{Squaring both sides}\ begin{array}{l} sin ^{4} theta+cos ^{4} theta \ =1-2 sin ^{2} theta cdot cos ^{2} theta \ operatorname{Put} theta=90^{circ} \ =1-2 sin ^{2}...

Maximum value of 2sinθ + 3cosθ is? A. 2 B. $sqrt{13}$ C. $sqrt{15}$ D. 1 Answer: Option B Show Answer Solution(By Apex Team) $begin{array}{l}(2sintheta+3costheta)\ text{Maximum value of}\ asintheta+bcostheta\ begin{array}{l} =sqrt{a^{2}+b^{2}} \ =sqrt{2^{2}+3^{2}} \ =sqrt{4+9} \ =sqrt{13} end{array}end{array}$

The minimum value of $2 sin ^{2} theta+3 cos ^{2} theta$ is ? A. 0 B. 3 C. 2 D. 1 Answer: Option C Show Answer Solution(By Apex Team) Let the mother's present age be x years Then, the person's present age $begin{array}{l} text { Let }...