Question

prove cot square theta -tan squre theta=cosec squre theta-sec squre theta

Answer 1

Step-by-step explanation:

Solution :-

On taking LHS

cot² θ - tan² θ

We know that

cosec² θ - cot² θ = 1 and

sec² θ - tan² θ = 1

=> (cosec² θ - 1 )-(sec² θ - 1)

=> cosec² θ - 1 - sec² θ + 1

=> cosec² θ - sec² θ +(1-1)

=> cosec² θ - sec² θ +(0)

=> cosec² θ - sec² θ

=> RHS

=> LHS = RHS

Therefore,

cot² θ - tan² θ = cosec² θ - sec² θ

Hence, Proved.

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Solution :-

On taking LHS

cot² θ - tan² θ

We know that

cosec² θ - cot² θ = 1 and

sec² θ - tan² θ = 1

=> (cosec² θ - 1 )-(sec² θ - 1)

=> cosec² θ - 1 - sec² θ + 1

=> cosec² θ - sec² θ +(1-1)

=> cosec² θ - sec² θ +(0)

=> cosec² θ - sec² θ

=> RHS

=> LHS = RHS

Therefore,

cot² θ - tan² θ = cosec² θ - sec² θ

Hence, Proved.

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