In a , Prove that: (A+B)= ( -C)=0 - Vidyadip

Question

In a $\triangle\text{ABC},$ Prove that:
$\cos(\text{A+B})= \cos (\pi-\text{C})=0$

✓

Answer

We have: $\text{A + B + C}= \pi$ $\big(\because $ sum of 3 anglesof a triangle is $\pi=180^\circ\big)$
$\Rightarrow \text{A+B}=\pi-\text{C}$
$\Rightarrow \cos(\text{A+B})= \cos (\pi-\text{C})$
$\Rightarrow -\cos\text{C}$ $(\because\cos(\pi-\theta)=-\cos\theta)$
$\Rightarrow \cos(\text{A+B})+\cos\text{C}=0$
$\text{Proved}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find:

$\text{P}(\text{A}\cup\text{B})$
$\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$
$\text{P}(\overline{\text{A}}\cap{\text{B}})$
$\text{P}({\text{A}}\cap\overline{\text{B}})$

Evaluate the following:
$\frac{1}{\text{i}^{58}}$

Find co-ordinates of focus, equation of directrix, length of latus rectum and the co-ordinates of end points of latus rectum of the parabola:

$y^2=-20 x$

The radius of a circle is 9 cm. Find the length of an arc of this circle which cuts off a chord of length equal to length of radius.

15 professors have been invited for a round table conference by the Vice-chancellor of a university. What is the probability that two particular professors occupy the seats on either side of the Vice-chancellor during the conference?

The origin is shifted to the point $(-2,1)$, the axes being parallel to the original axes. If the new co-ordinates of point $\mathrm{A}$ are $(7,-4)$, find the old co-ordinates of point $\mathrm{A}$.

Find:
The $12^{th}$ term of the G.P. $\frac{1}{\text{a}^3\text{x}^3},\text{ax},\text{a}^5\text{x}^5\dots$

Show the following quadratic equation by factorization method:
$x^2 + x + 1 = 0$

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

List all the element of the following sets:
E = {x : x is a month of a year not having 31 days};