yes and yes.
you're told ∠A=∠B. this means angle A and B are equal. so the value you get for cos A will be the same as the value you'll get for cos B
also, the value you get for tan A will be the same as the value you'll get for tan B
if that doesn't make sense you could also draw the triangle and solve for A and B.
you're told it's a right angled triangle meaning one of the angles = 90
you're told that C is that angle so if C is a right angle, angle C=90
the sum of all the angles in a triangle = 180
so angle A+ angle B + angle C = 180
angle A+ angle B + 90 = 180
angle A+ angle B = 180 - 90
angle A+ angle B = 90
- A and B could be any value but you're told angle A = angle B
angle A+ angle B = 90
you can divide 90 by 2 because A and B are equal. that will give you 45 for A and 45 for B
or
since angle A = angle B,
1. you can substitute angle A with angle B like this
angle B+ angle B = 90
2 angle B = 90
angle B = 90/2
angle B=45; ∴ angle A is also 45 ( because angle A= angle B)
2. or you could substitute angle B with angle A
angle A+ angle A = 90
2 angle A = 90
angle A = 90/2
angle A =45; ∴ angle B is also 45 ( because angle A= angle B)
Now you know what A and B are,
sin A = sin 45; sin B = sin 45
sin 45 = sin 45
tan A = tan 45; tan B = tan 45
tan 45 = tan 45
