Question

Fast guys...plz help​

Answer 1

Here,

(cos30°+sin60°)/(1+cos30°sin60°)

=(√3/2+√3/2)/(1+√3/2×√3/2)

=(2√3/2)(1+3/4)

=(2√3/2)(7/4)

=14√3/8

=7√3/4

Hope this will help you.

Answer 2

${ \tt{ \huge {Question \colon}}}$

${ \rm{ \dfrac{ cos30 \degree+ \: sin 60 \degree}{1 + \: cos30 \degree sin 60 \degree} }}$

${ \tt{ \huge {Solution \colon}}}$

${ \rm{ \dfrac{ \dfrac{ \sqrt{3} }{2} + \dfrac{ \sqrt{3} }{2} }{ 1 + \dfrac{ \sqrt{3} }{2} \times \dfrac{ \sqrt{3} }{2} } }}$

${ \rm{ = \dfrac{ \dfrac{ \sqrt{3} + \sqrt{3} }{2} }{1 + \dfrac{3}{4} } }}$

${ \rm{ = \dfrac{ \dfrac{2 \sqrt{3} }{2} }{ \dfrac{4 + 3}{4} } }}$

${ \rm{ = \dfrac{ \sqrt{3} }{ \dfrac{7}{4} } }}$

${ \rm{ = \sqrt{3} \times \dfrac{4}{7} }}$

${ \rm{ = \dfrac{4 \sqrt{3} }{7} }}$

──────────────────────────

${ \rm{ \large more \: related \: formulas}}$

${ \rm{(i) {sin}^{2} \theta + {cos}^{2} \theta = 1 }}$

${ \rm{(ii) {sec}^{2} \theta - {tan}^{2} \theta = 1 }}$

${ \rm{(iii) {cosec}^{2} \theta - {cot}^{2} \theta = 1 }}$

${ \rm{ sin \theta= \dfrac{p}{h} }}$

${ \rm{ cos \theta= \dfrac{b}{h} }}$

${ \rm{ tan \theta= \dfrac{p}{b} }}$

${ \rm{ cosec \theta= \dfrac{h}{p} }}$

${ \rm{ sec \theta= \dfrac{h}{b} }}$

${ \rm{ cot \theta= \dfrac{b}{p} }}$

${ \rm{where}}$

${ \rm{p = perpendicular}}$

${ \rm{b = base}}$

${ \rm{h = hypotense}}$