Answer:
Step-by-step explanation:
Required to prove that:
Sin θ(Sec θ + Cosec θ)= tan θ+1
Steps:
Recall sec θ= 1/cos θ and cosec θ=1/sin θ
Substitution into the Left Hand Side gives:
Sin θ(Sec θ + Cosec θ)
= Sin θ(1/cos θ + 1/sinθ )
Expanding the Brackets
=sinθ/cos θ + sinθ/sinθ
=tanθ+1 which is the Right Hand Side as required.
Note that from trigonometry sinθ/cosθ = tan θ
The value of x is 2 because we can compare like terms
y = 5 x +3 is the final equation when y = 5 x 3 units up
<u>Step-by-step explanation:</u>
In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.
Here we have , y=5x . Function y = 5x is a straight line passing through origin and having a slope of 5 . Now we need to increment this function 3 units up i.e. y = 5x + 3 , This a straight line passing through x-axis at 
and y-axis at 3. For your reference , following graph of y= 5x and y = 5x + 3 is attached .
Answer:
Yes
Step-by-step explanation:
Yes , if both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram . The parallelogram has opposite sides equal and parallel . Diagonals bisect each other . The sum of alternate angles is 180° and the opposite angles are equal .
Answer:
7.8 feet
Step-by-step explanation:
The shadow, the ground and the distance between the top of the tree and end of the shadow form 2 right-angled triangles which are similar.
So corresponding sides are in the same ratio. Therefore:-
40 / 12 = 26/x where x is the length of shadow cast by the smaller tree.
40x = 12*26
x = (12*26) / 40
= 7.8 feet
