Answer:
Step-by-step explanation:
1.
cot x sec⁴ x = cot x+2 tan x +tan³x
L.H.S = cot x sec⁴x
=cot x (sec²x)²
=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]
= cot x(1+ 2 tan²x +tan⁴x)
=cot x+ 2 cot x tan²x+cot x tan⁴x
=cot x +2 tan x + tan³x [ ∵cot x tan x 
=1]
=R.H.S
2.
(sin x)(tan x cos x - cot x cos x)=1-2 cos²x
L.H.S =(sin x)(tan x cos x - cot x cos x)
= sin x tan x cos x - sin x cot x cos x
= sin²x -cos²x
=1-cos²x-cos²x
=1-2 cos²x
=R.H.S
3.
1+ sec²x sin²x =sec²x
L.H.S =1+ sec²x sin²x
=
[
]
=1+tan²x ![[\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%5Ctextrm%7Bsin%20x%7D%7D%7B%5Ctextrm%7Bcos%20x%7D%7D%20%3D%20%5Ctextrm%7Btan%20x%7D%5D)
=sec²x
=R.H.S
4.
L.H.S=
= 2 csc x
= R.H.S
5.
-tan²x + sec²x=1
L.H.S=-tan²x + sec²x
= sec²x-tan²x
=
=1
Answer:6,051
Step-by-step explanation:1+2+3+2,014+2,015+2,016
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What is 36/40 Simplified? - 9/10 is the simplified fraction for 36/40.
Answer:
Q : 3
10x - 11 = 120 - 11 = 109°
3x - 2 = 36 - 2 = 34°
3x + 1 = 36 + 1 = 37°
Q ; 2
3x - 5 = 27 - 5= 22°
7x + 5 = 63 + 5 = 68°
And 90°
Q1 :
∠1 = 92°
∠2 = 42°
∠3 = 113°
Step-by-step explanation:
Solution for Q : 3
As the angle of all three is given as ,
10x - 11
3x - 2
3x + 1
We know sum of all the three angles of triangle = 180 °
So, (10x - 11) + (3x - 2) + (3x + 1) = 180°
Or, 16x - 12 = 180°
Or 16x = 192°, So , x = 12
So, all three angles are 10x - 11 = 120 - 11 = 109°
3x - 2 = 36 - 2 = 34°
3x + 1 = 36 + 1 = 37°
Solution for Q - 2
Given angles are
3x - 5
7x + 5
90°
We know sum of all the three angles of triangle = 180 °
so ,(3x - 5) + (7x + 5) + 90 = 180°
or 10x = 180 - 90 = 90°
SO, x = 9°
SO, all the three angles are 3x - 5 = 27 - 5= 22°
7x + 5 = 63 + 5 = 68°
And 90°
Solution for Q : 1
From,
the shown fig it is clear that
The ∠2 = 42° (<u> opposite vertical angles</u> )
so, in left triangle
50° + ∠2 + ∠1 = 180°
Or, 50° + 42° + ∠1 = 180° ( sum of all angles of triangles = 180°)
Or, ∠1 = 92°
Again
From right figure triangle
∠2 + 25° + ∠3 = 180°
Or, 42° + 25° + ∠3 = 180
Or, ∠3 = 113°
