Find the exact value of cos(a + b), given sin a = 2/5 for a in Quadrant || and cos B = 1/3 for b in Quadrant IV.

Option (4)

Step-by-step explanation:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b) [Identity]

Since, sin(a) = for a in quadrant II

Therefore, cos(a) =

cos(a) =

But cosine of a is negative quadrant II

Therefore, cos(a) = -

And cos(b) = for b in quadrant IV

Therefore, sin(b) =

                           =

                           =

But sine of an angle is negative in quadrant IV,

Therefore, sin(b) =

Now substituting these values in the identity,

cos(a + b) =

                =

                =

Therefore, Option (4) will be the answer.  

i need a picure

step-by-step explanation:

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for