Question

12. In a right-angled triangle, it is given that A is
5
an acute angle and tan A =
12
Find the values of :
(i) cos A
(ii) sin A (iii)
COS A + sinA ———————
COS A - sin A
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Answer 1

Answer:

i) cos A = 12/13

ii) sin A = 5/13

iii) cos A + sin A = 17/13

iv) cos A - sin A = 7/13

Step-by-step explanation:

Hii mate :-)

Given, tan A = 5/12

i) We know that,

  1 + tan²A = sec²A

  =>1 + (5/12)² = sec²A

  =>sec²A = 1 + 25/144

              = (144+25)/144

              = 169/144

  =>sec A = √(169/144)

             = 13/12

  => cos A = 1 / sec A

  => cos A = 12/13

ii) sin A = √(1-cos²A)

         = √[1-(12/13)²]

         = √[1-(144/169)]

         = √[(169-144)/169]

         = √(25/169)

  => sin A = 5/13

iii) cos A + sin A = (12/13) + (5/13)

                           = (12+5)/13

  => cos A + sin A = 17/13

iv) cos A - sin A = (12/13) - (5/13)

                          = (12-5)/13

  => cos A - sin A = 7/13

HOPE IT HELPS,

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Answer 2

Answer:

i) 12/13

ii) 5/13

iii) 17/13

iv) 7/13