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sin²Ф/cos²Ф + cos²Ф/sin²Ф = X [Since,tanФ=sinФ/cosФ & cotФ=cosФ/sinФ]

(sin²Ф.cos²Ф + cos²Ф.sin²Ф) / cos²Ф.sin²Ф = X [By taking LCM]

2 sin²Ф.cos²Ф / sin²Ф.cosФ = X [By division]

sin²Ф.cos²Ф = X

(sinФ.cosФ)² = X

sinФ cosФ = √X

1/(sinФ cosФ) = 1/√X