Question

step by step explain make it fast​

Answer 1

Answer:

in rt angled triangle ADB

in which AD=2. BD=4. AB=?

By PGT

H2=B2+P2

AB2=4+16

AB2=20

AB=√20

Now sec A=B/H= 2/√20

Answer 2

Answer:

$AD=2, \: CD=3, \: BD=4\\(AB)²=(AD)²+(BD)² \\ (AB)²=(2)²+(4)² \\ </p><p>(AB)²=4+16 \\ (AB)²=20 \\ AB= \sqrt{20} \\ AB=2 \sqrt{5} \\(BC)²=(BD)²+(CD)² \\ (BC)²=(4)²+(3)² \\ (BC)²=16+9 \\ (BC)²=25 \\ BC= \sqrt{25} \\ BC=5 \\ i)secA \\ = \frac{AB}{AD} \\ =\frac{2 \sqrt{5} }{2} \\ = \sqrt{5} \\ ii)tanC \\ = \frac{BD}{CD} \\ = \frac{4}{3} \\ iii)secC \\ =\frac{BC}{CD} \\ = \frac{5}{3} \\ iv)sec²C-tan²C \\ = { (\frac{5}{3} )}^{2} - { (\frac{4}{3} )}^{2} \\ =\frac{25}{9} - \frac{16}{9} \\ = \frac{25 - 16}{9} \\ = \frac{9}{9} \\ =1$