Question

5cosA + 12sinA=13,show that tanA=12\5

Answer 1

5 Cos@ +12 Sin@ = 13
on squaring both sides
25 Cos^2@ +144 Sin^2@ +120Cos@ Sin@ = 169
or 25(1-Sin^2@ )+144(1- Sin^2@)+120Cos@ Sin@ = 169
or 25-25 Sin^2@ +144- 144 Sin^2@+120Cos@ Sin@ = 169
or 169-25 Sin^2@ - 144 Sin^2@+120Cos@ Sin@ = 169
or 25 Sin^2@ + 144 Sin^2@-120Cos@ Sin@=0
or (5 Sin@ -12Cos@)^2=0
or 5 Sin@ -12 Cos@=0
or 5 Sin@ =12 Cos@
or tan@ =12/5=2.4

Answer 2

Here is your answer-

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