Projection Formula

Q.

How do you simplify $\cot x+\tan x$?

Q.

Prove that$(secA+\tan A)(1-\sin A)=\cos A$

Q.

$Inany\Delta ABC,\text{prove that :}a(cosB+cosC-1)+b(cosC+cosA-1)+c(cosA+cosB-1)=0$

Q. Integrate (pi/4 to 3pi/4) : x dx/(1+sinx)

Q.

Prove $\frac{(1+\cos A)}{\sin A}+\frac{(\sin A)}{(1+\cos A)}=2\mathrm{cosec}A$

Q. 40. Lim \sqrt{}a+2x - \sqrt{}3x÷ \sqrt{}3a+x-2\sqrt{}x x-0

Q. 15. Integration over (COSx+SINx).dx

Q. Find the real value of x, such that ((1-isinx)/(1+2isinx)) is (i) purely real (ii) purely imaginary

Q. 31. Integrate the following: (a) \sqrt{}2 - 1 (b) 1 / ( \sqrt{}2 - 1 ) (c) π / ( \sqrt{}2 + 1 ) (d) π / ( \sqrt{}2 - 1 )

Q.

In a $\Delta ABC$, side b is equal to

1. c Cos A + a cos C

2. a cos B + b cos A

3. b cos C + c cos B

4. None of these

Q.

$Ina\Delta ABC,\text{prove that}si{n}^{3}Acos(B-C)+si{n}^{3}Bcos(C-A)+si{n}^{3}Ccos(A-B)=3sinAsinBsinC$

Q. In $△$ ABC, cosec A(sin B cos C + cos B sin C) =

1. c/a
2. a/c
3. 1
4. c/ab

Q. 4. Integration sinxd(cosx) is equal to

Q. In a triangle ABC, b cosC + c cos B is always less than b + c.

1. False
2. True

Q. \lim_{x-2} x-2/\sqrt x -\sqrt{2 find balu

Q. $Sin3x+sin2x-sinx=4sinx\frac{cosx}{2}\frac{cos3x}{2}$

Q.

In a $\Delta ABC$, side b is equal to

1. c Cos A + a cos C

2. a cos B + b cos A

3. b cos C + c cos B

4. None of these

Q. If the area of the triangle $ABC$ is $\Delta ,$ such that $b^2\sin 2C+c^2\sin 2B=k\Delta ,$ then the value of $k$ is

Q. In $△$ ABC, cosec A(sin B cos C + cos B sin C) =

1. c/a
2. a/c
3. 1
4. c/ab

Q. In a triangle ABC, b cosC + c cos B is always less than b + c.

1. True
2. False

Q. sqrt x -sqrt 1- x^2 domain ?

Q. In triangle ABC, (b+c)cos A + (c+a) cos B + (a+b) cos C = [MP PET 1985]

1. 0
2. 1
3. a + b + c
4. 2(a+b+c)

Q. In triangle ABC, (b+c)cos A + (c+a) cos B + (a+b) cos C = [MP PET 1985]

1. \N
2. 1
3. a + b + c
4. 2(a+b+c)

Q.

How do you use the fundamental trigonometric identities to determine the simplified form of the expression?

Q. In a triangle ABC , $2(bco{s}^2\frac{C}{2}+cco{s}^2\frac{B}{2})$ is equal to -

1. a + b + c
2. $a^2+b^2+c^2$
3. a.b.c
4. None of these

Q. In $△$ ABC, cosec A(sin B cos C + cos B sin C) =

1. c/a
2. a/c
3. 1
4. c/ab

Q.

Find the value of $\left(\frac{7}{co{t}^2\theta }-\frac{7}{{\cos }^2\theta }\right)$.

Q.

Determine whether the following equation is identity or not:

${\cos }^2\mathrm{\theta }-{\sin }^2\mathrm{\theta }=\frac{2\mathrm{tan\theta }}{1+{\tan }^2\mathrm{\theta }}$.

Q.

How do you prove $\cos \left(\frac{\mathrm{\pi }}{7}\right)\cos \left(\frac{2\mathrm{\pi }}{7}\right)\cos \left(\frac{3\mathrm{\pi }}{7}\right)=\frac{1}{8}$?