Question

Any maths lover in brainly ¿¿¿¿¿
if s thn solve it guyzZ!!!!​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

L.H.S

cot θ - tan θ

Use cot θ = cos θ / sin θ

Use tan θ = sin θ / cos θ

⇒ cos θ / sin θ - sin θ / cos θ

⇒ ( cos²θ - sin²θ ) / ( sin θ cos θ )

Use sin²θ + cos²θ = 1  , then 2 cos²θ - 1 = cos²θ - sin²θ

⇒ ( 2 cos²θ - 1 ) / ( sin θ cos θ )

L.H.S = R.H.S .

Hence Proved !

sin θ ( 1  + tan θ ) + cos θ ( 1 + cot θ )

Use tan θ = sin θ/cos θ and cot θ = cos θ/sin θ :

⇒ sin θ ( 1 + sinθ/cosθ ) + cos θ ( 1 + cosθ/sinθ )

⇒ sin θ ( cos θ + sin θ )/cos θ + cos θ ( sin θ + cos θ )/sin θ

⇒ ( sin θ + cos θ )[ sin θ/cos θ + cos θ/sin θ ]

⇒ ( sin θ + cos θ ) [ sin² θ + cos² θ ] / sin θcos θ

Use sin² θ + cos² θ = 1 :

⇒ ( sin θ + cos  θ ) / sin θ cos θ

⇒ sin θ / sin θ cos θ + cos θ / sin θ cos θ

⇒ 1/cos θ + 1/sin θ

Use 1/cos θ = sec θ and 1/sin θ = cosec θ

⇒ sec θ + cosec θ

L.H.S = R.H.S

Hence proved .