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Step-by-step explanation:
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Answer:
see explanation
Step-by-step explanation:
Using sum to product identities
cos x - cos y = - 2sin(
)sin(
) = 2sin(
)sin(
)
cos x + cos y = 2cos(
)cos(
)
Note that
sin10° = sin(90 - 10)° = cos80°
Thus
← cancel 2 from numerator/ denominator
=
× 
= tan45° × tan35° { tan45° = 1 ]
= 1 × tan35°
= tan35° ← as required
Answer:

Step-by-step explanation:
Given;
x² - 2x - 1 = 0
Solve by completing the square method;
⇒ take the constant to the right hand side of the equation.
x² - 2x = 1
⇒ take half of coefficient of x = ¹/₂ x -2 = -1
⇒ square half of coefficient of x and add it to the both sides of the equation


⇒ take the square root of both sides;

Therefore, option B is the right solution.
Answer:
7 inches.
Step-by-step explanation:
Longest book length - Shortest book length


To put an equation into (x+c)^2, we need to see if the trinomial is a perfect square.
General form of a trinomial: ax^2+bx+c
If c is a perfect square, for example (1)^2=1, 2^2=4, that's a good indicator that it's a perfect square trinomial.
Here, it is, because 1 is a perfect square.
To ensure that it's a perfect square trinomial, let's look at b, which in this case is 2.
It has to be double what c is.
2 is the double of 1, therefore this is a perfect square trinomial.
Knowing this, we can easily put it into the form (x+c)^2.
And the answer is: (x+1)^2.
To do it the long way:
x^2+2x+1
Find 2 numbers that add to 2 and multiply to 1.
They are both 1.
x^2+x+x+1
x(x+1)+1(x+1)
Gather like terms
(x+1)(x+1)
or (x+1)^2.