Question

Q- (1+ tan A + sec A) (1+cot A
- cosec A) = 2​

Answer 1

Step-by-step explanation:

(1+tanA+ secA)(1+cotA-cosecA)

=1+sinA/cosA+ 1/cosA)(1+cosA/sinA- 1/sinA)

=(cosA+sinA+1)/cosA ×(sinA+cosA-1)/sinA

=(cosA.sinA+cos²A-cosA+sin²A+sinA.cosA-sinA+sinA+cosA-1)/sinA.cosA

=(2cosA.sinA+1-1)/sinA.cosA (sin²A+cos²A=1)

=2cosA.sinA/sinA.cosA

=2

= R.H.S

Answer 2

$\huge\mathrm{Answer}$

⭐ cos²A + sin²A = 1

⭐ a² - b² = ( a + b )( a - b )

Rules :-

$\boxed{☆ \:By \: using \: a \: right-angled \: triangle \: as \: a \: reference, \: the \: trigonometric \: functions \: or \: identities \: are \: derived \: : \: sin θ \: = \: Opposite \: Side \: / \: Hypotenuse. \: cos θ \: = \: Adjacent \: Side \: / \: Hypotenuse. \: tan \: θ = /: Opposite \: Side \: / \: Adjacent \: Side.\:)}$

cos θ = cosine

sin θ = sine

tan θ = tangent

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★ sin²θ + cos²θ = 1

★ tan²θ + 1 = sec²θ

★ cot²θ + 1 = cosec²θ