Question

if tanA = 4/3, then prove that √(1-sinA)÷√(1+sinA) = ½

Answer 1

3tanA=4or, tanA=4/3=p/bUsing Pythagorus theorem, h²=p²+b² we get,h²=4²+3²or, h²=16+9or, h²=25or, h=5 (neglecting the negative sign)∴, secA=h/b=5/3 and cosecA=h/p=5/4i) √secA-cosecA/√secA+cosecA=√(5/3-5/4)/(5/3+5/4)=√(5/12)/√(35/12)=√(5/12×12/35)=√1/7ii) 1-sinA/1+cosA=(1-4/5)/(1+3/5)={(5-4)/5}/{(5+3)/5}=(1/5)/(8/5)=1/5×5/8=1/8
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Answer 2

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