**Master TRICK IN REMEMBERING TRIGONOMETRIC FORMULAS in 5 Minutes A Day**: Trigonometric formulas can seem overwhelming at first, but with some practice and the right approach, they can be easy to remember. Here’s a simple trick you can use to remember the basic trigonometric formulas:

**Draw a right-angled triangle and label its sides as follows:**- The hypotenuse is always opposite the right angle and is labeled ‘h’.
- The side adjacent to the angle you are interested in is labeled ‘a’.
- The side opposite to the angle you are interested in is labeled ‘o’.

**Remember the acronym ‘SOHCAHTOA’, which stands for:**- Sine = Opposite/Hypotenuse
- Cosine = Adjacent/Hypotenuse
- Tangent = Opposite/Adjacent

**To remember the reciprocals of these trigonometric functions, remember the acronym ‘CAHSHOA’, which stands for:**- Cosecant = Hypotenuse/Opposite
- Secant = Hypotenuse/Adjacent
- Cotangent = Adjacent/Opposite

**To remember the Pythagorean identity, remember the formula:**- sin²θ + cos²θ = 1
- You can also remember it as ‘SohCahToa squared equals one.’

**To remember the angle sum and difference identities, remember the formulas:**- sin(α ± β) = sinα cosβ ± cosα sinβ
- cos(α ± β) = cosα cosβ ∓ sinα sinβ
- tan(α ± β) = (tanα ± tanβ) / (1 ∓ tanα tanβ)

Yes!! There are many tricks that I have figured out myself (I don’t know about others).. First of all, for basic ratio, if you are an Indian, you will love this sentence (xD) :

Pakistan bhookha pyaasa ,

Hindustan hara bhara.

Take the first initials of words in first line and divide them by corresponding initials of word in second line.

P/h b/h p/b

and the sequence is

sinx cosx tanx

assign these ratios..

sinx= p/h

cosx=b/h

tanx=p/b

where, p= perpendicular ,b= base and h= hypotenuse

[I was taught this sentence in class ten and now still I use this sentence in class XII]

Also, you need to learn

**1/sinx = cosec x**

**1/cosx= secx**

**1/tanx= cot x**

Now, coming to other formulas, you first need to remember the most basic formula of trigonometry:

**sin²x+cos²x=1** —(1)

*now, divide(1) by cos²x,*

**tan²x+1=sec²x**

*and also, divide (1) by sin²x*

**1+cot²x=cosec²x**

Now, for remembering values, you just need to remember valued of sin and you can figure out the rest(I will tell)

**Steps to get values of sin(0–90):**

*write down 0,30,45,60,90 in a single line (horizontally)**just below it write 0,1,2,3,4 below these values in the same way**divide these values (0,1,2,3,4) by 4.**now take square root of these values**you will get the values of sin**now reverse the order for cos**divide corresponding value of sin with cos and write them for tan*

Generate a table like this and see the values corresponding to angle of sin/cos/tan.

*For cosec/sec/cot, divide divide 1 by these values for example cot 45=1/tan45 =1.*

Now, there comes some more formulas..

**sin(x+y)= sinx.cosy+cosx.siny**

**sin(x-y)= sinx.cosy-cosx.siny**

**cos(x+y)= cosx.cosy-sinx.siny**

**cos(x-y)= cosx.cosy+sinx.siny**

*now for formula of sin 2x*, from sin(x+y),

sin(x+x)= sinx.cosx+ sinx.cosx

**sin 2x= 2sinx.cosx**

*for cos 2x*, from cos(x+y)

cos(x+x)= cosx.cosx – sinx.sinx

**cos 2x= cos²x-sin²x**

but, sin²x+cos²x=1,

so, sin²x=1-cos²x

*putting in cos 2x,*

**cos 2x= cos²x-1+cos²x**

**cos 2x= 2 cos²x-1**

also, cos²x=1- sin²x [from (1)]

**cos 2x=1-sin²x-sin²x**

**cos 2x=1–2sin²x**

Well, this way, all formulas are inter-related and you can derive them whenever you need if you know the right trick. This makes trigonometry easier!(There are more formulas which you need to remember also)

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Thanks for reading!