Question

if tanA = cot (60+A), find the value of A​

Answer 1

$in \: trigonmetry \: the \: ratio \: \\ can \: be \: converted \\ \: to \: other \: forms \: in \: terms \: of \: 90\: \\ \\ we \: know \: that \: \\ \tan( \alpha ) = \cot(90 - \alpha ) \\ applying \: this \: concept \\ \: in \: the \: given \: question \\ \: we \: will \: get \: a \: linear \: equation \\ \: in \: terms \: of \: a \\ \: which \: we \: can \: easily \: solve \\ \: to \: get \: the \: required \: value \: of \: a \\ lets \: do \: so \\ \\ now \: putting \: \tan(a) = \cot(90 - a) \\ we \: get \\ \cot(90 - a) = \cot(60 + a) \\ since \: the \: ratio \: are \: same \: we \: can \: write \: it \: as \\ 90 - a = 60 + a \\ we \: now \: get \\ 30 = 2a \\ a = \frac{30}{2} \\ a = 15 \\ \\ we \: get \\ \: the \: required \: vlue \: of \: a \: is \: 15$

Answer 2

Step-by-step explanation:

cot (90-A)=tan A

90-A=60+A

2A=30

A=15