Question

20. If 3 tan A = 4 then prove that
sec A-cosec A 1
(i)
sec A+ cosec A 7
1-sin A 1
1+cos A 2√2
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Answer 1

$\huge{\underline{\underline{\bf{\purple{answer}}}}}$

3TanA = 4

TanA = 4/3 = P/B

USING PYTHAGORAS THEOREM ,

H^2 = P^2 + B^2

WHERE ,

H = Hypotenuse

B = BASE

P = Perpendicular

H^2 = 4^3 + 3^3

H^2 = 16 + 9

H^2 = 25

H = _/25 = 5cm

______________________

SinA = P/H = 4/5

CosA = B/H = 3/5

TanA = P/B = 4/3

______________________

CosecA = H/P = 5/4

SecA = H/P = 5/3

CotA = B/P = 3/4

______________________

1) SecA - CosecA1

= 5/3 - 5/4

= ( 20 - 15 )/12

= 5/12

______________________

2) SecA + CosecA7

= 5/3 + (5/4)7

= 5/3 + 35/4

= ( 20 + 105 )/12

= 125/12

______________________

3) 1 - SinA

= 1 - 4/5

= (5 - 4)/5

= 1/5

______________________

4) 1 + CosA 2_/2

= 1 + ( 4/5 )2_/2

= 1 + (8_/2)/5

= ( 5 + 8_/2 )/ 5

______________________

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