Question

alpha + beta=90°, than prove that sin beta + sec alpha/sin alpha= tan alpha +2tan beta...​

Answer 1

Answer:

α+β=90

sin(α)

sec(α)+sin(β)

=tan(α)+2tan(β)

rhs

=tan(α)+2tan(β)

=

cos(α)

sin(α)

+2

cos(β)

sin(β)

=

cos(α)cos(β)

sin(α)cos(β)+2sin(β)cos(α)

=

cos(α)cos(90−α)

sin(α)cos(90−α)+2sin(β)cos(α)

=

cos(α)sin(α)

sin(α)sin(α)+2sin(β) cos(α)

=

cos(α)sin(α)

1−cos(α)

2

+2sin(β)cos(α)

=

cos(α)sin(α)

1

+

sin(α)

−cos(α)+2sin(β)

=

cos(α)sin(α)

1

+

sin(α)

−cos(90−β)+2sin(β)

=

cos(α)sin(α)

1

+

sin(α)

sin(β)

=

sin(α)

sec(α)

+

sin(α)

sin(β)

=

sin(α)

sec(α)+sin(β)

=lhs

proved