InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
CosA 0.6,show that(5sinA-3tanA)=0 |
| Answer» Given,\xa0cos{tex}\\theta{/tex}\xa0= 0.6\xa0{tex}= \\frac { 6 } { 10 } = \\frac { 3 } { 5 }{/tex}Let us draw a triangle ABC in which\xa0{tex}\\angle{/tex}B =\xa090°.Let\xa0{tex}\\angle{/tex}A =\xa0{tex}\\theta{/tex}°.Then,\xa0{tex}\\cos \\theta = \\frac { A B } { A C } = \\frac { 3 } { 5 }{/tex}Let AB = 3k and AC = 5k, where k is positive.By Pythagoras\' theorem, we haveAC2\xa0= AB2 + BC2{tex}\\Rightarrow{/tex}BC2\xa0= AC2\xa0- AB2\xa0= (5k)2\xa0- (3k)2\xa0= 25k2\xa0- 9k2\xa0= 16k2{tex}\\Rightarrow \\quad B C = \\sqrt { 16 k ^ { 2 } } = 4 k{/tex}{tex}\\sin \\theta = \\frac { A B } { A C } = \\frac { 4 k } { 5 k } = \\frac { 4 } { 5 }{/tex}{tex}\\cos \\theta = \\frac { 3 } { 5 }{/tex}{tex}\\tan \\theta = \\frac { \\sin \\theta } { \\cos \\theta } = \\left( \\frac { 4 } { 5 } \\times \\frac { 5 } { 3 } \\right) = \\frac { 4 } { 3 }{/tex}{tex}\\Rightarrow ( 5 \\sin \\theta - 3 \\tan \\theta ) = \\left( 5 \\times \\frac { 4 } { 5 } - 3 \\times \\frac { 4 } { 3 } \\right) = 0{/tex}Hence,\xa0(5sin{tex}\\theta{/tex}\xa0- 3 tan{tex}\\theta{/tex}) = 0. | |