Solution: (i) We can write the given question as, $\sin ^{-1} \frac{1}{2}-2 \sin ^{-1} \frac{1}{\sqrt{2}}=\sin ^{-1} \frac{1}{2}-\sin ^{-1}\left(2 \times \frac{1}{\sqrt{2}}...
Solution: (i) It is given that functions can be written as $\sin ^{-1}\left(\frac{\sqrt{3}-1}{2 \sqrt{2}}\right)=\sin ^{-1}\left(\frac{\sqrt{3}}{2 \sqrt{2}}-\frac{1}{2 \sqrt{2}}\right) $Taking $1 /...
(iii) Let us consider, Age of Rohan’s = x years Therefore, as per the given question, Rohan’s mother’s age = x + 26 After 3 years, Age of Rohan’s = x + 3 Age of Rohan’s mother will be = x + 26 + 3...
Solutions: (i) Let us consider, Breadth of the rectangular plot = x m Thus, the length of the plot = (2x + 1) m. As we know, $Area\text{ }of\text{ }rectangle\text{ }=\text{ }length~\times...
$\left( vii \right)\text{ }Given,\text{ }{{\left( x~+\text{ }2 \right)}^{3}}~=\text{ }2x({{x}^{2}}~\text{ }1)$ By using the formula for ${{\left( a+b \right)}^{2~}}=\text{ }{{a}^{2}}+2ab+{{b}^{2}}$...
(i) Given, (2x – 1)(x – 3) = (x + 5)(x – 1) By using the formula for (a+b)2=a2+2ab+b2 ⇒ 2x2 – 7x + 3 = x2 + 4x – 5 ⇒ x2 – 11x + 8 = 0 Since the above equation is in the form of ax2 + bx + c = 0....
$\left( iii \right)\text{ }Given,\text{ }\left( x\text{ }\text{ }2 \right)\left( x\text{ }+\text{ }1 \right)\text{ }=\text{ }\left( x\text{ }\text{ }1 \right)\left( x\text{ }+\text{ }3 \right)$ By...
(i) Given, (x + 1)2 = 2(x – 3) By using the formula for (a+b)2 = a2+2ab+b2 ⇒ x2 + 2x + 1 = 2x – 6 ⇒ x2 + 7 = 0 Since the above equation is in the form of ax2 + bx + c = 0. Therefore, the given...
(i) All circles are ____________ (congruent, similar). (ii) All squares are ___________ (similar, congruent). (iii) All ____________ triangles are similar (isosceles, equilaterals). (iv) Two...